diff --git a/.github/workflows/build-and-test-linux.yml b/.github/workflows/build-and-test-linux.yml
index 8fc36a039..f850c4cfd 100644
--- a/.github/workflows/build-and-test-linux.yml
+++ b/.github/workflows/build-and-test-linux.yml
@@ -160,12 +160,12 @@ jobs:
           elif [[ "${{ matrix.compiler }}" == 'clang' ]]; then
             export CC=clang
             export CXX=clang++
-            export FC=gfortran-13
+            export FC=gfortran-12
             export LDFLAGS='-fuse-ld=lld'
           elif [[ "${{ matrix.compiler }}" == 'gcc' ]]; then
-            export CC=gcc-13
-            export CXX=g++-13
-            export FC=gfortran-13
+            export CC=gcc-12
+            export CXX=g++-12
+            export FC=gfortran-12
           fi
           if [[ "${{ matrix.math-libs }}" == 'aocl' ]]; then
             export AOCLROOT=/opt/AMD/aocl/aocl-linux-gcc-4.1.0/gcc
diff --git a/CHANGELOG.md b/CHANGELOG.md
index 4fb80fc63..d26fe6ad2 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -11,7 +11,7 @@ The format of this changelog is based on
 [Keep a Changelog](https://keepachangelog.com/en/1.0.0/), and this project adheres to
 [Semantic Versioning](https://semver.org/).
 
-## In progress
+## [0.13.0] - 2024-05-20
 
   - Changed default value of `config["Solver"]["PartialAssemblyOrder"]` in order to activate
     operator partial assembly by default for all operators in all simulation types.
@@ -33,7 +33,7 @@ The format of this changelog is based on
     [Parallelism and GPU support](https://awslabs.github.io/palace/dev/guide/parallelism/).
   - Removed use of `mfem::SparseMatrix` and replaced with HYPRE's `hypre_CSRMatrix` when
     needed for full assembly, wrapped as `palace::hypre::HypreCSRMatrix`.
-  - Added `"Active"`` configuration file parameter for lumped and wave port boundaries to
+  - Added `"Active"` configuration file parameter for lumped and wave port boundaries to
     disable the associated boundary condition and only use the surface for postprocessing.
   - Changed the smooth flux space for the electrostatic error estimator to fix performance
     on problems with material interfaces.
diff --git a/CMakeLists.txt b/CMakeLists.txt
index fd4101cf9..00546f040 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -14,7 +14,7 @@ if(CMAKE_SOURCE_DIR STREQUAL CMAKE_BINARY_DIR)
 endif()
 
 # Initialize the project
-project(palace-superbuild LANGUAGES CXX C VERSION 0.12.0)
+project(palace-superbuild LANGUAGES CXX C VERSION 0.13.0)
 
 # Define build settings and defaults
 set(PALACE_WITH_64BIT_INT OFF CACHE BOOL "Use 64 bit integers")
diff --git a/cmake/ExternalGitTags.cmake b/cmake/ExternalGitTags.cmake
index a066d01e2..b90f6e7f9 100644
--- a/cmake/ExternalGitTags.cmake
+++ b/cmake/ExternalGitTags.cmake
@@ -34,7 +34,7 @@ set(EXTERN_BUTTERFLYPACK_GIT_BRANCH
   "Git branch for external ButterflyPACK build"
 )
 set(EXTERN_BUTTERFLYPACK_GIT_TAG
-  "6bb36d00ad8deab43d74aa4fce0715e9400d994a" CACHE STRING
+  "7410fca61c188daab40f55c235ab7fad16ee5856" CACHE STRING
   "Git tag for external ButterflyPACK build"
 )
 
@@ -76,7 +76,7 @@ set(EXTERN_LIBCEED_GIT_BRANCH
   "Git branch for external libCEED build"
 )
 set(EXTERN_LIBCEED_GIT_TAG
-  "1809c5f74680557a641e900d791842bafdfb4e8b" CACHE STRING
+  "ef9a992f4cf09f2be4ec72f649495c67ec03f813" CACHE STRING
   "Git tag for external libCEED build"
 )
 
@@ -90,7 +90,7 @@ set(EXTERN_LIBXSMM_GIT_BRANCH
   "Git branch for external LIBXSMM build"
 )
 set(EXTERN_LIBXSMM_GIT_TAG
-  "feacc5e2112af47a0f4669e4ba20f0d01c08f944" CACHE STRING
+  "953405207f32369cd74d757681ce476fe89768b6" CACHE STRING
   "Git tag for external LIBXSMM build"
 )
 
@@ -132,7 +132,7 @@ set(EXTERN_MFEM_GIT_BRANCH
   "Git branch for external MFEM build"
 )
 set(EXTERN_MFEM_GIT_TAG
-  "7c296d00d8a770e9f569e4db9d7e6d415902a886" CACHE STRING  # master @ 05/09/2024
+  "c444b17c973cc301590a6ac186fb33587b5881e6" CACHE STRING  # master @ 05/18/2024
   "Git tag for external MFEM build"
 )
 
@@ -146,7 +146,7 @@ set(EXTERN_MUMPS_GIT_BRANCH
   "Git branch for external MUMPS build"
 )
 set(EXTERN_MUMPS_GIT_TAG
-  "cbdf7fc5d5bd5471a55459e92fc8b5fd1f16f651" CACHE STRING
+  "b00cc7c9fc6127e07d6583a8c50c727508ea1c6e" CACHE STRING
   "Git tag for external MUMPS build"
 )
 
@@ -174,7 +174,7 @@ set(EXTERN_PETSC_GIT_BRANCH
   "Git branch for external PETSc build"
 )
 set(EXTERN_PETSC_GIT_TAG
-  "3d77ad52841f320b3f6ad02ce14f35e73e722480" CACHE STRING
+  "e6938432041f05a2617386d95f6ba21e1677d3e7" CACHE STRING
   "Git tag for external PETSc build"
 )
 
@@ -202,7 +202,7 @@ set(EXTERN_SLEPC_GIT_BRANCH
   "Git branch for external SLEPc build"
 )
 set(EXTERN_SLEPC_GIT_TAG
-  "1b1a6e4c08bfc150112594b09cc439adf16f4899" CACHE STRING
+  "2c2766ada27519a79c9f9d9634b730afb4010d95" CACHE STRING
   "Git tag for external SLEPc build"
 )
 
@@ -230,7 +230,7 @@ set(EXTERN_SUPERLU_GIT_BRANCH
   "Git branch for external SuperLU_DIST build"
 )
 set(EXTERN_SUPERLU_GIT_TAG
-  "c6896d85b22384880db409ba042a03966530678e" CACHE STRING
+  "2e39ceca001f594dc63426f2b500c82f5ce312a3" CACHE STRING
   "Git tag for external SuperLU_DIST build"
 )
 
@@ -244,7 +244,7 @@ set(EXTERN_ZFP_GIT_BRANCH
   "Git branch for external ZFP build"
 )
 set(EXTERN_ZFP_GIT_TAG
-  "6814a4ebbbee6002f1d7f39a0acc9e8429545bce" CACHE STRING
+  "6aa2dae1c1bf700f062f386e81cc71796929c30e" CACHE STRING
   "Git tag for external ZFP build"
 )
 
diff --git a/examples/coaxial/mesh/mesh.jl b/examples/coaxial/mesh/mesh.jl
index 50fcaa180..52c6dd11b 100644
--- a/examples/coaxial/mesh/mesh.jl
+++ b/examples/coaxial/mesh/mesh.jl
@@ -41,7 +41,7 @@ function generate_coaxial_mesh(;
     @assert outer_diameter_mm > inner_diameter_mm > 0
     @assert length_mm > 0
     @assert refinement >= 0
-    @assert order > 1
+    @assert order > 0
 
     kernel = gmsh.model.occ
 
diff --git a/examples/cpw/cpw_coax_adaptive.json b/examples/cpw/cpw_coax_adaptive.json
new file mode 100644
index 000000000..0c9c40f11
--- /dev/null
+++ b/examples/cpw/cpw_coax_adaptive.json
@@ -0,0 +1,173 @@
+{
+  "Problem":
+  {
+    "Type": "Driven",
+    "Verbose": 2,
+    "Output": "postpro/coax_adaptive"
+  },
+  "Model":
+  {
+    "Mesh": "mesh/cpw_coax_0.msh",
+    "L0": 1.0e-6,  // μm
+    "Refinement": {}
+  },
+  "Domains":
+  {
+    "Materials":
+    [
+      {
+        "Attributes": [1],  // Air
+        "Permeability": 1.0,
+        "Permittivity": 1.0,
+        "LossTan": 0.0
+      },
+      {
+        "Attributes": [2],  // Sapphire
+        "Permeability": [0.99999975, 0.99999975, 0.99999979],
+        "Permittivity": [9.3, 9.3, 11.5],
+        "LossTan": [3.0e-5, 3.0e-5, 8.6e-5],
+        "MaterialAxes": [[0.8, 0.6, 0.0], [-0.6, 0.8, 0.0], [0.0, 0.0, 1.0]]
+      }
+    ],
+    "Postprocessing":
+    {
+      "Energy":
+      [
+        {
+          "Index": 1,
+          "Attributes": [2]
+        }
+      ],
+      "Probe":
+      [
+        {
+          "Index": 1,
+          "Center": [2000, 833, 30]
+        },
+        {
+          "Index": 2,
+          "Center": [2000, 833, -30]
+        }
+      ]
+    }
+  },
+  "Boundaries":
+  {
+    "PEC":
+    {
+      "Attributes": [8, 9, 11]  // Metal trace + end boundaries
+    },
+    "Absorbing":
+    {
+      "Attributes": [10],
+      "Order": 1
+    },
+    "LumpedPort":
+    [
+      {
+        "Index": 1,
+        "Attributes": [4],
+        "Direction": "+R",
+        "R": 56.02,  // Ω
+        "Excitation": true
+      },
+      {
+        "Index": 2,
+        "Attributes": [5],
+        "Direction": "+R",
+        "R": 56.02  // Ω
+      },
+      {
+        "Index": 3,
+        "Attributes": [6],
+        "Direction": "+R",
+        "R": 56.02  // Ω
+      },
+      {
+        "Index": 4,
+        "Attributes": [7],
+        "Direction": "+R",
+        "R": 56.02  // Ω
+      }
+    ],
+    "Postprocessing":
+    {
+      "SurfaceFlux":
+      [
+        {
+          "Index": 1,
+          "Attributes": [11],
+          "Type": "Electric",
+          "TwoSided": true
+        },
+        {
+          "Index": 2,
+          "Attributes": [10],
+          "Type": "Power"
+        },
+        {
+          "Index": 3,
+          "Attributes": [4, 6, 8],
+          "Type": "Power",
+          "Center": [-2000, 0, 0]
+        },
+        {
+          "Index": 4,
+          "Attributes": [5, 7, 9],
+          "Type": "Power",
+          "Center": [2000, 0, 0]
+        }
+      ],
+      "Dielectric":
+      [
+        {
+          "Index": 1,
+          "Attributes": [12],
+          "Type": "SA",
+          "Thickness": 2.0e-3,  // μm
+          "Permittivity": 10.0,
+          "LossTan": 1.0
+        },
+        {
+          "Index": 2,
+          "Attributes": [11],
+          "Type": "MS",
+          "Thickness": 2.0e-3,  // μm
+          "Permittivity": 10.0,
+          "LossTan": 1.0,
+          "Side": "LargerRefractiveIndex"
+        },
+        {
+          "Index": 3,
+          "Attributes": [11],
+          "Type": "MA",
+          "Thickness": 2.0e-3,  // μm
+          "Permittivity": 10.0,
+          "LossTan": 1.0,
+          "Side": "SmallerRefractiveIndex"
+        }
+      ]
+    }
+  },
+  "Solver":
+  {
+    "Order": 2,
+    "Device": "CPU",
+    "Driven":
+    {
+      "MinFreq": 2.0,  // GHz
+      "MaxFreq": 30.0,  // GHz
+      "FreqStep": 0.1,  // GHz
+      "SaveStep": 40,
+      "AdaptiveTol": 1.0e-3
+    },
+    "Linear":
+    {
+      "Type": "Default",
+      "KSPType": "GMRES",
+      "Tol": 1.0e-8,
+      "MaxIts": 200
+    }
+  }
+}
+
diff --git a/examples/cpw/cpw_coax_uniform.json b/examples/cpw/cpw_coax_uniform.json
new file mode 100644
index 000000000..c05878e75
--- /dev/null
+++ b/examples/cpw/cpw_coax_uniform.json
@@ -0,0 +1,172 @@
+{
+  "Problem":
+  {
+    "Type": "Driven",
+    "Verbose": 2,
+    "Output": "postpro/coax_uniform"
+  },
+  "Model":
+  {
+    "Mesh": "mesh/cpw_coax_0.msh",
+    "L0": 1.0e-6,  // μm
+    "Refinement": {}
+  },
+  "Domains":
+  {
+    "Materials":
+    [
+      {
+        "Attributes": [1],  // Air
+        "Permeability": 1.0,
+        "Permittivity": 1.0,
+        "LossTan": 0.0
+      },
+      {
+        "Attributes": [2],  // Sapphire
+        "Permeability": [0.99999975, 0.99999975, 0.99999979],
+        "Permittivity": [9.3, 9.3, 11.5],
+        "LossTan": [3.0e-5, 3.0e-5, 8.6e-5],
+        "MaterialAxes": [[0.8, 0.6, 0.0], [-0.6, 0.8, 0.0], [0.0, 0.0, 1.0]]
+      }
+    ],
+    "Postprocessing":
+    {
+      "Energy":
+      [
+        {
+          "Index": 1,
+          "Attributes": [2]
+        }
+      ],
+      "Probe":
+      [
+        {
+          "Index": 1,
+          "Center": [2000, 833, 30]
+        },
+        {
+          "Index": 2,
+          "Center": [2000, 833, -30]
+        }
+      ]
+    }
+  },
+  "Boundaries":
+  {
+    "PEC":
+    {
+      "Attributes": [8, 9, 11]  // Metal trace + end boundaries
+    },
+    "Absorbing":
+    {
+      "Attributes": [10],
+      "Order": 1
+    },
+    "LumpedPort":
+    [
+      {
+        "Index": 1,
+        "Attributes": [4],
+        "Direction": "+R",
+        "R": 56.02,  // Ω
+        "Excitation": true
+      },
+      {
+        "Index": 2,
+        "Attributes": [5],
+        "Direction": "+R",
+        "R": 56.02  // Ω
+      },
+      {
+        "Index": 3,
+        "Attributes": [6],
+        "Direction": "+R",
+        "R": 56.02  // Ω
+      },
+      {
+        "Index": 4,
+        "Attributes": [7],
+        "Direction": "+R",
+        "R": 56.02  // Ω
+      }
+    ],
+    "Postprocessing":
+    {
+      "SurfaceFlux":
+      [
+        {
+          "Index": 1,
+          "Attributes": [11],
+          "Type": "Electric",
+          "TwoSided": true
+        },
+        {
+          "Index": 2,
+          "Attributes": [10],
+          "Type": "Power"
+        },
+        {
+          "Index": 3,
+          "Attributes": [4, 6, 8],
+          "Type": "Power",
+          "Center": [-2000, 0, 0]
+        },
+        {
+          "Index": 4,
+          "Attributes": [5, 7, 9],
+          "Type": "Power",
+          "Center": [2000, 0, 0]
+        }
+      ],
+      "Dielectric":
+      [
+        {
+          "Index": 1,
+          "Attributes": [12],
+          "Type": "SA",
+          "Thickness": 2.0e-3,  // μm
+          "Permittivity": 10.0,
+          "LossTan": 1.0
+        },
+        {
+          "Index": 2,
+          "Attributes": [11],
+          "Type": "MS",
+          "Thickness": 2.0e-3,  // μm
+          "Permittivity": 10.0,
+          "LossTan": 1.0,
+          "Side": "LargerRefractiveIndex"
+        },
+        {
+          "Index": 3,
+          "Attributes": [11],
+          "Type": "MA",
+          "Thickness": 2.0e-3,  // μm
+          "Permittivity": 10.0,
+          "LossTan": 1.0,
+          "Side": "SmallerRefractiveIndex"
+        }
+      ]
+    }
+  },
+  "Solver":
+  {
+    "Order": 2,
+    "Device": "CPU",
+    "Driven":
+    {
+      "MinFreq": 2.0,  // GHz
+      "MaxFreq": 30.0,  // GHz
+      "FreqStep": 2.0,  // GHz
+      "SaveStep": 2
+    },
+    "Linear":
+    {
+      "Type": "Default",
+      "KSPType": "GMRES",
+      "Tol": 1.0e-8,
+      "MaxIts": 200
+    }
+  }
+}
+
diff --git a/examples/cpw/mesh/cpw_coax.msh b/examples/cpw/mesh/cpw_coax.msh
new file mode 100644
index 000000000..67761c286
--- /dev/null
+++ b/examples/cpw/mesh/cpw_coax.msh
@@ -0,0 +1,50841 @@
+$MeshFormat
+2.2 0 8
+$EndMeshFormat
+$PhysicalNames
+13
+2 4 "port1"
+2 5 "port2"
+2 6 "port3"
+2 7 "port4"
+2 8 "end1"
+2 9 "end2"
+2 10 "farfield"
+2 11 "trace"
+2 12 "gap"
+2 13 "trace2"
+3 1 "air"
+3 2 "si"
+3 3 "metal"
+$EndPhysicalNames
+$Nodes
+27543
+1 0 0 1
+2 4000 0 1
+3 4000 800 1
+4 0 800 1
+5 0 866 1
+6 4000 866 1
+7 4000 1066 1
+8 0 1066 1
+9 0 1132 1
+10 4000 1132 1
+11 4000 1932 1
+12 0 1932 1
+13 0 818 1
+14 4000 818 1
+15 4000 848 1
+16 0 848 1
+17 0 1084 1
+18 4000 1084 1
+19 4000 1114 1
+20 0 1114 1
+21 0 0 -500
+22 0 1932 -500
+23 4000 0 -500
+24 4000 1932 -500
+25 0 -500 -1000
+26 0 -500 1000
+27 0 2432 -1000
+28 0 2432 1000
+29 0 800 0
+30 0 0 0
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+48 4000 -500 1000
+49 4000 2432 -1000
+50 4000 2432 1000
+51 4000 0 0
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+55 4000 1066 0
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+58 4000 800 0
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+60 4000 1113.966629547096 0.999999999999917
+61 4000 1099 15
+62 4000 1084.033370452904 0.9999999999999137
+63 4000 1084 0
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+65 4000 847.9666295470957 0.999999999999917
+66 4000 833 15
+67 4000 818.0333704529043 0.9999999999999137
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diff --git a/examples/cpw/mesh/cpw_coax_0.msh b/examples/cpw/mesh/cpw_coax_0.msh
new file mode 100644
index 000000000..85a16ac18
--- /dev/null
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+$EndElements
diff --git a/examples/cpw/mesh/mesh.jl b/examples/cpw/mesh/mesh.jl
index 705f01fd9..449418892 100644
--- a/examples/cpw/mesh/mesh.jl
+++ b/examples/cpw/mesh/mesh.jl
@@ -7,6 +7,7 @@ using Gmsh: gmsh
     function generate_cpw_wave_mesh(;
         filename::AbstractString,
         refinement::Integer       = 0,
+        order::Integer            = 1,
         trace_width_μm::Real      = 30.0,
         gap_width_μm::Real        = 18.0,
         separation_width_μm::Real = 200.0,
@@ -15,6 +16,7 @@ using Gmsh: gmsh
         metal_height_μm::Real     = 0.0,
         remove_metal_vol::Bool    = true,
         length_μm::Real           = 4000.0,
+        coax_ports::Bool          = false,
         verbose::Integer          = 5,
         gui::Bool                 = false
     )
@@ -25,6 +27,7 @@ Generate a mesh for the coplanar waveguide with wave ports using Gmsh
 
   - filename - the filename to use for the generated mesh
   - refinement - measure of how many elements to include, 0 is least
+  - order - the polynomial order of the approximation, minimum 1
   - trace_width_μm - width of the coplanar waveguide trace, in μm
   - gap_width_μm - width of the coplanar waveguide gap, in μm
   - separation_width_μm - separation distance between the two waveguides, in μm
@@ -33,12 +36,14 @@ Generate a mesh for the coplanar waveguide with wave ports using Gmsh
   - metal_height_μm - metal thickness, in μm
   - remove_metal_vol - for positive metal thickness, whether to remove the metal domain
   - length_μm - length of the waveguides, in μm
+  - coax_ports - flag to use coaxial lumped ports instead of wave ports
   - verbose - flag to dictate the level of print to REPL, passed to Gmsh
   - gui - whether to launch the Gmsh GUI on mesh generation
 """
 function generate_cpw_wave_mesh(;
     filename::AbstractString,
     refinement::Integer       = 0,
+    order::Integer            = 1,
     trace_width_μm::Real      = 30.0,
     gap_width_μm::Real        = 18.0,
     separation_width_μm::Real = 200.0,
@@ -47,10 +52,12 @@ function generate_cpw_wave_mesh(;
     metal_height_μm::Real     = 0.0,
     remove_metal_vol::Bool    = true,
     length_μm::Real           = 4000.0,
+    coax_ports::Bool          = false,
     verbose::Integer          = 5,
     gui::Bool                 = false
 )
     @assert refinement >= 0
+    @assert order > 0
     @assert trace_width_μm > 0
     @assert gap_width_μm > 0
     @assert separation_width_μm > 0
@@ -135,37 +142,66 @@ function generate_cpw_wave_mesh(;
         separation_width_μm +
         gap_width_μm +
         0.5 * trace_width_μm
-    dyp1 = 0.5 * (cy2 - cy1)
-    dyp2 = dyp1
-    dzp1 = 0.5 * (sep_dz + substrate_height_μm)
-    dzp2 = substrate_height_μm
-    let pa, pb, l
-        pa = kernel.addPoint(0.0, cy1 - dyp2, -dzp1)
-        pb = kernel.addPoint(0.0, cy1 + dyp1, -dzp1)
-        l = kernel.addLine(pa, pb)
-        global p1 =
-            first(filter(x -> x[1] == 2, kernel.extrude([1, l], 0.0, 0.0, dzp1 + dzp2)))[2]
-    end
-    let pa, pb, l
-        pa = kernel.addPoint(0.0, cy2 - dyp1, -dzp1)
-        pb = kernel.addPoint(0.0, cy2 + dyp2, -dzp1)
-        l = kernel.addLine(pa, pb)
-        global p3 =
-            first(filter(x -> x[1] == 2, kernel.extrude([1, l], 0.0, 0.0, dzp1 + dzp2)))[2]
-    end
-    let pa, pb, l
-        pa = kernel.addPoint(length_μm, cy1 - dyp2, -dzp1)
-        pb = kernel.addPoint(length_μm, cy1 + dyp1, -dzp1)
-        l = kernel.addLine(pa, pb)
-        global p2 =
-            first(filter(x -> x[1] == 2, kernel.extrude([1, l], 0.0, 0.0, dzp1 + dzp2)))[2]
-    end
-    let pa, pb, l
-        pa = kernel.addPoint(length_μm, cy2 - dyp1, -dzp1)
-        pb = kernel.addPoint(length_μm, cy2 + dyp2, -dzp1)
-        l = kernel.addLine(pa, pb)
-        global p4 =
-            first(filter(x -> x[1] == 2, kernel.extrude([1, l], 0.0, 0.0, dzp1 + dzp2)))[2]
+    if coax_ports
+        ra = 0.5 * trace_width_μm
+        rb = 0.5 * trace_width_μm + gap_width_μm
+        let da, db
+            da = kernel.addDisk(0.0, cy1, 0.0, ra, ra, -1, [1, 0, 0], [])
+            db = kernel.addDisk(0.0, cy1, 0.0, rb, rb, -1, [1, 0, 0], [])
+            global p1 = last(first(first(kernel.cut((2, db), (2, da)))))
+        end
+        let da, db
+            da = kernel.addDisk(0.0, cy2, 0.0, ra, ra, -1, [1, 0, 0], [])
+            db = kernel.addDisk(0.0, cy2, 0.0, rb, rb, -1, [1, 0, 0], [])
+            global p3 = last(first(first(kernel.cut((2, db), (2, da)))))
+        end
+        let da, db
+            da = kernel.addDisk(length_μm, cy1, 0.0, ra, ra, -1, [1, 0, 0], [])
+            db = kernel.addDisk(length_μm, cy1, 0.0, rb, rb, -1, [1, 0, 0], [])
+            global p2 = last(first(first(kernel.cut((2, db), (2, da)))))
+        end
+        let da, db
+            da = kernel.addDisk(length_μm, cy2, 0.0, ra, ra, -1, [1, 0, 0], [])
+            db = kernel.addDisk(length_μm, cy2, 0.0, rb, rb, -1, [1, 0, 0], [])
+            global p4 = last(first(first(kernel.cut((2, db), (2, da)))))
+        end
+    else
+        dyp1 = 0.5 * (cy2 - cy1)
+        dyp2 = dyp1
+        dzp1 = 0.5 * (sep_dz + substrate_height_μm)
+        dzp2 = substrate_height_μm
+        let pa, pb, l
+            pa = kernel.addPoint(0.0, cy1 - dyp2, -dzp1)
+            pb = kernel.addPoint(0.0, cy1 + dyp1, -dzp1)
+            l = kernel.addLine(pa, pb)
+            global p1 = first(
+                filter(x -> x[1] == 2, kernel.extrude([1, l], 0.0, 0.0, dzp1 + dzp2))
+            )[2]
+        end
+        let pa, pb, l
+            pa = kernel.addPoint(0.0, cy2 - dyp1, -dzp1)
+            pb = kernel.addPoint(0.0, cy2 + dyp2, -dzp1)
+            l = kernel.addLine(pa, pb)
+            global p3 = first(
+                filter(x -> x[1] == 2, kernel.extrude([1, l], 0.0, 0.0, dzp1 + dzp2))
+            )[2]
+        end
+        let pa, pb, l
+            pa = kernel.addPoint(length_μm, cy1 - dyp2, -dzp1)
+            pb = kernel.addPoint(length_μm, cy1 + dyp1, -dzp1)
+            l = kernel.addLine(pa, pb)
+            global p2 = first(
+                filter(x -> x[1] == 2, kernel.extrude([1, l], 0.0, 0.0, dzp1 + dzp2))
+            )[2]
+        end
+        let pa, pb, l
+            pa = kernel.addPoint(length_μm, cy2 - dyp1, -dzp1)
+            pb = kernel.addPoint(length_μm, cy2 + dyp2, -dzp1)
+            l = kernel.addLine(pa, pb)
+            global p4 = first(
+                filter(x -> x[1] == 2, kernel.extrude([1, l], 0.0, 0.0, dzp1 + dzp2))
+            )[2]
+        end
     end
     let pa, pb, l
         pa = kernel.addPoint(0.0, -sep_dy, -sep_dz)
@@ -365,7 +401,7 @@ function generate_cpw_wave_mesh(;
     end
 
     gmsh.model.mesh.generate(3)
-    gmsh.model.mesh.setOrder(1)
+    gmsh.model.mesh.setOrder(order)
 
     # Save mesh
     gmsh.option.setNumber("Mesh.MshFileVersion", 2.2)
@@ -409,6 +445,7 @@ end
     function generate_cpw_lumped_mesh(;
         filename::AbstractString,
         refinement::Integer       = 0,
+        order::Integer            = 1,
         trace_width_μm::Real      = 30.0,
         gap_width_μm::Real        = 18.0,
         separation_width_μm::Real = 200.0,
@@ -427,6 +464,7 @@ Generate a mesh for the coplanar waveguide with lumped ports using Gmsh
 
   - filename - the filename to use for the generated mesh
   - refinement - measure of how many elements to include, 0 is least
+  - order - the polynomial order of the approximation, minimum 1
   - trace_width_μm - width of the coplanar waveguide trace, in μm
   - gap_width_μm - width of the coplanar waveguide gap, in μm
   - separation_width_μm - separation distance between the two waveguides, in μm
@@ -441,6 +479,7 @@ Generate a mesh for the coplanar waveguide with lumped ports using Gmsh
 function generate_cpw_lumped_mesh(;
     filename::AbstractString,
     refinement::Integer       = 0,
+    order::Integer            = 1,
     trace_width_μm::Real      = 30.0,
     gap_width_μm::Real        = 18.0,
     separation_width_μm::Real = 200.0,
@@ -453,6 +492,7 @@ function generate_cpw_lumped_mesh(;
     gui::Bool                 = false
 )
     @assert refinement >= 0
+    @assert order > 0
     @assert trace_width_μm > 0
     @assert gap_width_μm > 0
     @assert separation_width_μm > 0
@@ -732,7 +772,7 @@ function generate_cpw_lumped_mesh(;
     end
 
     gmsh.model.mesh.generate(3)
-    gmsh.model.mesh.setOrder(1)
+    gmsh.model.mesh.setOrder(order)
 
     # Save mesh
     gmsh.option.setNumber("Mesh.MshFileVersion", 2.2)
diff --git a/extern/patch/mfem/patch_mesh_part_const.diff b/extern/patch/mfem/patch_mesh_part_const.diff
index ea000c64d..70567000f 100644
--- a/extern/patch/mfem/patch_mesh_part_const.diff
+++ b/extern/patch/mfem/patch_mesh_part_const.diff
@@ -1,35 +1,160 @@
+diff --git a/mesh/mesh.cpp b/mesh/mesh.cpp
+index e18def619..afee9d8f9 100644
+--- a/mesh/mesh.cpp
++++ b/mesh/mesh.cpp
+@@ -13600,22 +13600,23 @@ Mesh &MeshPart::GetMesh()
+ 
+ MeshPartitioner::MeshPartitioner(Mesh &mesh_,
+                                  int num_parts_,
+-                                 int *partitioning_,
++                                 const int *partitioning_,
+                                  int part_method)
+    : mesh(mesh_)
+ {
+    if (partitioning_)
+    {
+-      partitioning.MakeRef(partitioning_, mesh.GetNE(), false);
++      partitioning.MakeRef(const_cast<int *>(partitioning_), mesh.GetNE(),
++                           false);
+    }
+    else
+    {
+-      partitioning_ = mesh.GeneratePartitioning(num_parts_, part_method);
+       // Mesh::GeneratePartitioning always uses new[] to allocate the,
+       // partitioning, so we need to tell the memory manager to free it with
+       // delete[] (even if a different host memory type has been selected).
+-      const MemoryType mt = MemoryType::HOST;
+-      partitioning.MakeRef(partitioning_, mesh.GetNE(), mt, true);
++      constexpr MemoryType mt = MemoryType::HOST;
++      partitioning.MakeRef(mesh.GeneratePartitioning(num_parts_, part_method),
++                           mesh.GetNE(), mt, true);
+    }
+ 
+    Transpose(partitioning, part_to_element, num_parts_);
+diff --git a/mesh/mesh.hpp b/mesh/mesh.hpp
+index f328f6c29..1431a484e 100644
+--- a/mesh/mesh.hpp
++++ b/mesh/mesh.hpp
+@@ -2726,8 +2726,8 @@ public:
+                                 Mesh::GeneratePartitioning() when the provided
+                                 input partitioning is NULL.
+    */
+-   MeshPartitioner(Mesh &mesh_, int num_parts_, int *partitioning_ = NULL,
+-                   int part_method = 1);
++   MeshPartitioner(Mesh &mesh_, int num_parts_,
++                   const int *partitioning_ = nullptr, int part_method = 1);
+ 
+    /** @brief Construct a MeshPart corresponding to the given @a part_id.
+ 
 diff --git a/mesh/nurbs.cpp b/mesh/nurbs.cpp
-index 32223524c..b156fecaf 100644
+index 06c80c967..8ab5e5650 100644
 --- a/mesh/nurbs.cpp
 +++ b/mesh/nurbs.cpp
-@@ -4730,7 +4730,7 @@ ParNURBSExtension::ParNURBSExtension(const ParNURBSExtension &orig)
+@@ -4722,19 +4722,15 @@ const Array<int>& NURBSExtension::GetPatchBdrElements(int patch)
+ #ifdef MFEM_USE_MPI
+ ParNURBSExtension::ParNURBSExtension(const ParNURBSExtension &orig)
+    : NURBSExtension(orig),
+-     partitioning(orig.partitioning ? new int[orig.GetGNE()] : NULL),
++     partitioning(orig.partitioning),
+      gtopo(orig.gtopo),
+      ldof_group(orig.ldof_group)
+ {
+-   // Copy the partitioning, if not NULL
+-   if (partitioning)
+-   {
+-      std::memcpy(partitioning, orig.partitioning, orig.GetGNE()*sizeof(int));
+-   }
  }
  
  ParNURBSExtension::ParNURBSExtension(MPI_Comm comm, NURBSExtension *parent,
 -                                     int *part, const Array<bool> &active_bel)
-+                                     const int *part, const Array<bool> &active_bel)
++                                     const int *partitioning_,
++                                     const Array<bool> &active_bel)
     : gtopo(comm)
  {
     if (parent->NumOfActiveElems < parent->NumOfElements)
+@@ -4772,11 +4768,11 @@ ParNURBSExtension::ParNURBSExtension(MPI_Comm comm, NURBSExtension *parent,
+    CountElements();
+    CountBdrElements();
+ 
+-   // copy 'part' to 'partitioning'
+-   partitioning = new int[GetGNE()];
++   // copy 'partitioning_' to 'partitioning'
++   partitioning.SetSize(GetGNE());
+    for (int i = 0; i < GetGNE(); i++)
+    {
+-      partitioning[i] = part[i];
++      partitioning[i] = partitioning_[i];
+    }
+    SetActive(partitioning, active_bel);
+ 
+@@ -4867,8 +4863,6 @@ ParNURBSExtension::ParNURBSExtension(NURBSExtension *parent,
+ 
+    delete parent;
+ 
+-   partitioning = NULL;
+-
+    MFEM_VERIFY(par_parent->partitioning,
+                "parent ParNURBSExtension has no partitioning!");
+ 
 diff --git a/mesh/nurbs.hpp b/mesh/nurbs.hpp
-index 54aa364a1..65ef12d51 100644
+index b1c772bd3..7212774e9 100644
 --- a/mesh/nurbs.hpp
 +++ b/mesh/nurbs.hpp
-@@ -624,7 +624,8 @@ public:
+@@ -872,7 +872,7 @@ class ParNURBSExtension : public NURBSExtension
+ {
+ private:
+    /// Partitioning of the global elements by MPI rank
+-   int *partitioning;
++   mfem::Array<int> partitioning;
+ 
+    /// Construct and return a table of DOFs for each global element.
+    Table *GetGlobalElementDofTable();
+@@ -882,9 +882,10 @@ private:
  
+    /** @brief Set active global elements and boundary elements based on MPI
+        ranks in @a partition and the array @a active_bel. */
+-   void SetActive(const int *partition, const Array<bool> &active_bel);
++   void SetActive(const int *partitioning_, const Array<bool> &active_bel);
++
+    /// Set up GroupTopology @a gtopo for MPI communication.
+-   void BuildGroups(const int *partition, const Table &elem_dof);
++   void BuildGroups(const int *partitioning_, const Table &elem_dof);
+ 
+ public:
+    GroupTopology gtopo;
+@@ -895,11 +896,12 @@ public:
     ParNURBSExtension(const ParNURBSExtension &orig);
  
--   ParNURBSExtension(MPI_Comm comm, NURBSExtension *parent, int *partitioning,
+    /** @brief Constructor for an MPI communicator @a comm, a global
+-       NURBSExtension @a parent, a partitioning @a part of the global elements
+-       by MPI rank, and a marker @a active_bel of active global boundary
+-       elements on this rank. The partitioning is deep-copied and will not be
+-       deleted by this object. */
+-   ParNURBSExtension(MPI_Comm comm, NURBSExtension *parent, int *part,
++       NURBSExtension @a parent, a partitioning @a partitioning_ of the global
++       elements by MPI rank, and a marker @a active_bel of active global
++       boundary elements on this rank. The partitioning is deep-copied and will
++       not be deleted by this object. */
 +   ParNURBSExtension(MPI_Comm comm, NURBSExtension *parent,
-+                     const int *partitioning,
++                     const int *partitioning_,
                       const Array<bool> &active_bel);
  
-    // Create a parallel version of 'parent' with partitioning as in
+    /** @brief Create a parallel version of @a parent with partitioning as in
+@@ -907,8 +909,6 @@ public:
+        The @a parent can be either a local NURBSExtension or a global one. */
+    ParNURBSExtension(NURBSExtension *parent,
+                      const ParNURBSExtension *par_parent);
+-
+-   virtual ~ParNURBSExtension() { delete [] partitioning; }
+ };
+ #endif
+ 
 diff --git a/mesh/pmesh.cpp b/mesh/pmesh.cpp
-index 46ceb35e2..a46d9e315 100644
+index 46ceb35e2..9556bcbd2 100644
 --- a/mesh/pmesh.cpp
 +++ b/mesh/pmesh.cpp
-@@ -103,13 +103,13 @@ ParMesh& ParMesh::operator=(ParMesh &&mesh)
+@@ -103,29 +103,32 @@ ParMesh& ParMesh::operator=(ParMesh &&mesh)
     return *this;
  }
  
@@ -41,34 +166,39 @@ index 46ceb35e2..a46d9e315 100644
     , gtopo(comm)
  {
 -   int *partitioning = NULL;
-+   const int *partitioning = partitioning_ ? partitioning_ : nullptr;
-    Array<bool> activeBdrElem;
- 
+-   Array<bool> activeBdrElem;
+-
     MyComm = comm;
-@@ -118,18 +118,16 @@ ParMesh::ParMesh(MPI_Comm comm, Mesh &mesh, int *partitioning_,
+    MPI_Comm_size(MyComm, &NRanks);
+    MPI_Comm_rank(MyComm, &MyRank);
  
++   Array<int> partitioning;
++   Array<bool> activeBdrElem;
++
++   if (partitioning_)
++   {
++      partitioning.MakeRef(const_cast<int *>(partitioning_), mesh.GetNE(),
++                           false);
++   }
++
     if (mesh.Nonconforming())
     {
 -      if (partitioning_)
 -      {
 -         partitioning = partitioning_;
 -      }
-       ncmesh = pncmesh = new ParNCMesh(comm, *mesh.ncmesh, partitioning);
+-      ncmesh = pncmesh = new ParNCMesh(comm, *mesh.ncmesh, partitioning);
+-      if (!partitioning)
++      ncmesh = pncmesh = new ParNCMesh(comm, *mesh.ncmesh, partitioning_);
 +
-       if (!partitioning)
++      if (!partitioning_)
        {
 -         partitioning = new int[mesh.GetNE()];
-+         int *part = new int[mesh.GetNE()];
++         partitioning.SetSize(mesh.GetNE());
           for (int i = 0; i < mesh.GetNE(); i++)
           {
--            partitioning[i] = pncmesh->InitialPartition(i);
-+            part[i] = pncmesh->InitialPartition(i);
-          }
-+         partitioning = part;
-       }
- 
-       pncmesh->Prune();
-@@ -158,11 +156,7 @@ ParMesh::ParMesh(MPI_Comm comm, Mesh &mesh, int *partitioning_,
+             partitioning[i] = pncmesh->InitialPartition(i);
+@@ -158,13 +161,14 @@ ParMesh::ParMesh(MPI_Comm comm, Mesh &mesh, int *partitioning_,
  
        ncmesh = pncmesh = NULL;
  
@@ -77,11 +207,31 @@ index 46ceb35e2..a46d9e315 100644
 -         partitioning = partitioning_;
 -      }
 -      else
-+      if (!partitioning)
++      if (!partitioning_)
        {
-          partitioning = mesh.GeneratePartitioning(NRanks, part_method);
+-         partitioning = mesh.GeneratePartitioning(NRanks, part_method);
++         // Mesh::GeneratePartitioning always uses new[] to allocate the,
++         // partitioning, so we need to tell the memory manager to free it with
++         // delete[] (even if a different host memory type has been selected).
++         constexpr MemoryType mt = MemoryType::HOST;
++         partitioning.MakeRef(mesh.GeneratePartitioning(NRanks, part_method),
++                              mesh.GetNE(), mt, true);
        }
-@@ -730,7 +724,7 @@ void ParMesh::BuildVertexGroup(int ngroups, const Table &vert_element)
+ 
+       // re-enumerate the partitions to better map to actual processor
+@@ -306,11 +310,6 @@ ParMesh::ParMesh(MPI_Comm comm, Mesh &mesh, int *partitioning_,
+       SetVerticesFromNodes(Nodes);
+    }
+ 
+-   if (partitioning != partitioning_)
+-   {
+-      delete [] partitioning;
+-   }
+-
+    have_face_nbr_data = false;
+ }
+ 
+@@ -730,7 +729,7 @@ void ParMesh::BuildVertexGroup(int ngroups, const Table &vert_element)
  }
  
  void ParMesh::BuildSharedFaceElems(int ntri_faces, int nquad_faces,
@@ -91,7 +241,7 @@ index 46ceb35e2..a46d9e315 100644
                                     const Array<int> &face_group,
                                     const Array<int> &vert_global_local)
 diff --git a/mesh/pmesh.hpp b/mesh/pmesh.hpp
-index e33db8e43..44ce3be15 100644
+index e33db8e43..c6ceaed22 100644
 --- a/mesh/pmesh.hpp
 +++ b/mesh/pmesh.hpp
 @@ -241,7 +241,7 @@ protected:
@@ -108,7 +258,7 @@ index e33db8e43..44ce3be15 100644
         meshes (elements of nonconforming meshes should ideally be ordered as a
         sequence of face-neighbors). */
 -   ParMesh(MPI_Comm comm, Mesh &mesh, int *partitioning_ = NULL,
-+   ParMesh(MPI_Comm comm, Mesh &mesh, const int *partitioning_ = NULL,
++   ParMesh(MPI_Comm comm, Mesh &mesh, const int *partitioning_ = nullptr,
             int part_method = 1);
  
     /** Copy constructor. Performs a deep copy of (almost) all data, so that the
@@ -122,28 +272,85 @@ index e33db8e43..44ce3be15 100644
  
     ///@{ @name These methods require group > 0
 diff --git a/mesh/pncmesh.cpp b/mesh/pncmesh.cpp
-index 218faebfc..e90849e16 100644
+index 218faebfc..4b5b62096 100644
 --- a/mesh/pncmesh.cpp
 +++ b/mesh/pncmesh.cpp
-@@ -28,7 +28,7 @@ namespace mfem
+@@ -28,7 +28,8 @@ namespace mfem
  
  using namespace bin_io;
  
 -ParNCMesh::ParNCMesh(MPI_Comm comm, const NCMesh &ncmesh, int *part)
-+ParNCMesh::ParNCMesh(MPI_Comm comm, const NCMesh &ncmesh, const int *part)
++ParNCMesh::ParNCMesh(MPI_Comm comm, const NCMesh &ncmesh,
++                     const int *partitioning)
     : NCMesh(ncmesh)
  {
     MyComm = comm;
+@@ -39,7 +40,8 @@ ParNCMesh::ParNCMesh(MPI_Comm comm, const NCMesh &ncmesh, int *part)
+    // sequence of leaf elements into 'NRanks' parts
+    for (int i = 0; i < leaf_elements.Size(); i++)
+    {
+-      elements[leaf_elements[i]].rank = part ? part[i] : InitialPartition(i);
++      elements[leaf_elements[i]].rank =
++         partitioning ? partitioning[i] : InitialPartition(i);
+    }
+ 
+    Update();
 diff --git a/mesh/pncmesh.hpp b/mesh/pncmesh.hpp
-index 2f4e1eb74..497d73f93 100644
+index 2f4e1eb74..e4c54e8b6 100644
 --- a/mesh/pncmesh.hpp
 +++ b/mesh/pncmesh.hpp
-@@ -67,7 +67,7 @@ public:
+@@ -67,7 +67,8 @@ public:
     /// Construct by partitioning a serial NCMesh.
     /** SFC partitioning is used by default. A user-specified partition can be
         passed in 'part', where part[i] is the desired MPI rank for element i. */
 -   ParNCMesh(MPI_Comm comm, const NCMesh& ncmesh, int* part = NULL);
-+   ParNCMesh(MPI_Comm comm, const NCMesh& ncmesh, const int* part = NULL);
++   ParNCMesh(MPI_Comm comm, const NCMesh& ncmesh,
++             const int *partitioning = nullptr);
  
     /** Load from a stream, parallel version. See the serial NCMesh::NCMesh
         counterpart for a description of the parameters. */
+@@ -81,7 +82,8 @@ public:
+ 
+    /** An override of NCMesh::Refine, which is called eventually, after making
+        sure that refinements that occur on the processor boundary are sent to
+-       the neighbor processors so they can keep their ghost layers up to date.*/
++       the neighbor processors so they can keep their ghost layers up to
++       date. */
+    void Refine(const Array<Refinement> &refinements) override;
+ 
+    /// Parallel version of NCMesh::LimitNCLevel.
+@@ -229,8 +231,8 @@ public:
+                                     const Table &deref_table);
+ 
+    /** Extension of NCMesh::GetBoundaryClosure. Filters out ghost vertices and
+-       ghost edges from 'bdr_vertices' and 'bdr_edges', and uncovers hidden internal
+-       boundary faces. */
++       ghost edges from 'bdr_vertices' and 'bdr_edges', and uncovers hidden
++       internal boundary faces. */
+    void GetBoundaryClosure(const Array<int> &bdr_attr_is_ess,
+                            Array<int> &bdr_vertices,
+                            Array<int> &bdr_edges, Array<int> &bdr_faces) override;
+@@ -252,8 +254,9 @@ protected: // interface for ParMesh
+    friend class ParMesh;
+ 
+    /** For compatibility with conforming code in ParMesh and ParFESpace.
+-       Initializes shared structures in ParMesh: gtopo, shared_*, group_s*, s*_l*.
+-       The ParMesh then acts as a parallel mesh cut along the NC interfaces. */
++       Initializes shared structures in ParMesh: gtopo, shared_*, group_s*,
++       s*_l*. The ParMesh then acts as a parallel mesh cut along the NC
++       interfaces. */
+    void GetConformingSharedStructures(class ParMesh &pmesh);
+ 
+    /** Populate face neighbor members of ParMesh from the ghost layer, without
+@@ -519,8 +522,9 @@ protected: // implementation
+        owners, keeping the ghost layer up to date. Used by Rebalance() and
+        Derefine(). 'target_elements' is the number of elements this rank
+        is supposed to own after the exchange. If this number is not known
+-       a priori, the parameter can be set to -1, but more expensive communication
+-       (synchronous sends and a barrier) will be used in that case. */
++       a priori, the parameter can be set to -1, but more expensive
++       communication (synchronous sends and a barrier) will be used in that
++       case. */
+    void RedistributeElements(Array<int> &new_ranks, int target_elements,
+                              bool record_comm);
+ 
diff --git a/extern/patch/mfem/patch_nc_internal_bdr_project_fix.diff b/extern/patch/mfem/patch_nc_internal_bdr_project_fix.diff
index cb344e636..1770dd651 100644
--- a/extern/patch/mfem/patch_nc_internal_bdr_project_fix.diff
+++ b/extern/patch/mfem/patch_nc_internal_bdr_project_fix.diff
@@ -1,5 +1,5 @@
 diff --git a/fem/gridfunc.cpp b/fem/gridfunc.cpp
-index 6b2281c88..8223e185e 100644
+index 6b2281c88..778690091 100644
 --- a/fem/gridfunc.cpp
 +++ b/fem/gridfunc.cpp
 @@ -2061,41 +2061,37 @@ void GridFunction::AccumulateAndCountBdrValues(
@@ -117,7 +117,7 @@ index 6b2281c88..8223e185e 100644
                 if (++values_counter[ind] == 1)
                 {
                    (*this)(ind) = vals(k);
-@@ -2176,6 +2166,28 @@ void GridFunction::AccumulateAndCountBdrValues(
+@@ -2176,6 +2166,26 @@ void GridFunction::AccumulateAndCountBdrValues(
                 }
              }
           }
@@ -129,7 +129,6 @@ index 6b2281c88..8223e185e 100644
 +         if (vdofs.Size() == 0) { continue; }
 +
 +         ElementTransformation *transf = mesh->GetEdgeTransformation(edge);
-+         transf->Attribute = -1; // TODO: set the boundary attribute
 +         const FiniteElement *fe = fes->GetEdgeElement(edge);
 +         mark_dofs(*transf, *fe);
 +      }
@@ -140,13 +139,12 @@ index 6b2281c88..8223e185e 100644
 +         if (vdofs.Size() == 0) { continue; }
 +
 +         ElementTransformation *transf = mesh->GetFaceTransformation(face);
-+         transf->Attribute = -1; // TODO: set the boundary attribute
 +         const FiniteElement *fe = fes->GetFaceElement(face);
 +         mark_dofs(*transf, *fe);
        }
     }
  }
-@@ -2228,16 +2240,16 @@ void GridFunction::AccumulateAndCountBdrTangentValues(
+@@ -2228,26 +2238,37 @@ void GridFunction::AccumulateAndCountBdrTangentValues(
        accumulate_dofs(dofs, lvec, *this, values_counter);
     }
  
@@ -166,7 +164,10 @@ index 6b2281c88..8223e185e 100644
           fes->GetEdgeDofs(edge, dofs);
           if (dofs.Size() == 0) { continue; }
  
-@@ -2248,6 +2260,19 @@ void GridFunction::AccumulateAndCountBdrTangentValues(
+          T = mesh->GetEdgeTransformation(edge);
+-         T->Attribute = -1; // TODO: set the boundary attribute
+          fe = fes->GetEdgeElement(edge);
+          lvec.SetSize(fe->GetDof());
           fe->Project(vcoeff, *T, lvec);
           accumulate_dofs(dofs, lvec, *this, values_counter);
        }
@@ -177,7 +178,6 @@ index 6b2281c88..8223e185e 100644
 +         if (dofs.Size() == 0) { continue; }
 +
 +         T = mesh->GetFaceTransformation(face);
-+         T->Attribute = -1; // TODO: set the boundary attribute
 +         fe = fes->GetFaceElement(face);
 +         lvec.SetSize(fe->GetDof());
 +         fe->Project(vcoeff, *T, lvec);
@@ -187,20 +187,21 @@ index 6b2281c88..8223e185e 100644
  }
  
 diff --git a/tests/unit/mesh/test_ncmesh.cpp b/tests/unit/mesh/test_ncmesh.cpp
-index 1f6dd65fa..0d171d56a 100644
+index 1f6dd65fa..49f71739b 100644
 --- a/tests/unit/mesh/test_ncmesh.cpp
 +++ b/tests/unit/mesh/test_ncmesh.cpp
-@@ -1690,6 +1690,64 @@ TEST_CASE("Parallel RP=I", "[Parallel], [NCMesh]")
+@@ -2811,4 +2811,80 @@ TEST_CASE("RP=I", "[NCMesh]")
     }
  }
  
-+TEST_CASE("InternalBoundaryProjectBdrCoefficient", "[Parallel], [NCMesh]")
++
++TEST_CASE("InternalBoundaryProjectBdrCoefficient", "[NCMesh]")
 +{
-+   auto test_project_H1 = [](ParMesh &mesh,  int order, double coef)
++   auto test_project_H1 = [](Mesh &mesh,  int order, double coef)
 +   {
 +      H1_FECollection fe_collection(order, mesh.SpaceDimension());
-+      ParFiniteElementSpace fe_space(&mesh, &fe_collection);
-+      ParGridFunction x(&fe_space);
++      FiniteElementSpace fe_space(&mesh, &fe_collection);
++      GridFunction x(&fe_space);
 +      x = -coef;
 +      ConstantCoefficient c(coef);
 +
@@ -210,48 +211,63 @@ index 1f6dd65fa..0d171d56a 100644
 +      ess_bdr.Last() = 1; // internal boundary
 +      x.ProjectBdrCoefficient(c, ess_bdr);
 +
-+      Array<int> ess_tdofs_list;
-+      fe_space.GetEssentialTrueDofs(ess_bdr, ess_tdofs_list);
-+
-+      const auto &tvec = x.GetTrueVector();
-+      for (auto ess_dof : ess_tdofs_list)
++      Array<int> ess_vdofs_list, ess_vdofs_marker;
++      fe_space.GetEssentialVDofs(ess_bdr, ess_vdofs_marker);
++      fe_space.MarkerToList(ess_vdofs_marker, ess_vdofs_list);
++      for (auto ess_dof : ess_vdofs_list)
 +      {
-+         CHECK(tvec[ess_dof] == Approx(coef).epsilon(1e-8));
++         CHECK(x[ess_dof] == Approx(coef).epsilon(1e-8));
 +      }
 +
 +      int iess = 0;
-+      for (int i = 0; i < tvec.Size(); i++)
++      for (int i = 0; i < x.Size(); i++)
 +      {
-+         if (iess < ess_tdofs_list.Size() && i == ess_tdofs_list[iess])
++         if (iess < ess_vdofs_list.Size() && i == ess_vdofs_list[iess])
 +         {
 +            iess++;
 +            continue;
 +         }
-+         CHECK(tvec[i] == Approx(-coef).epsilon(1e-8));
++         CHECK(x[i] == Approx(-coef).epsilon(1e-8));
 +      }
++
++   };
++
++   auto OneSidedNCRefine = [](Mesh &mesh)
++   {
++      // Pick one element attached to the new boundary attribute and refine.
++      const auto interface_attr = mesh.bdr_attributes.Max();
++      Array<int> el_to_ref;
++      for (int nbe = 0; nbe < mesh.GetNBE(); nbe++)
++      {
++         if (mesh.GetBdrAttribute(nbe) == interface_attr)
++         {
++            int f, o, e1, e2;
++            mesh.GetBdrElementFace(nbe, &f, &o);
++            mesh.GetFaceElements(f, &e1, &e2);
++            el_to_ref.Append(e1);
++         }
++      }
++      mesh.GeneralRefinement(el_to_ref);
++      return;
 +   };
 +
 +   SECTION("Hex")
 +   {
 +      auto smesh = DividingPlaneMesh(false, true);
-+      smesh.EnsureNCMesh();
-+      ParMesh pmesh(MPI_COMM_WORLD, smesh);
-+      test_project_H1(pmesh, 1, 0.25);
-+      test_project_H1(pmesh, 2, 0.25);
-+      test_project_H1(pmesh, 3, 0.25);
++      smesh.EnsureNCMesh(true);
++      OneSidedNCRefine(smesh);
++      test_project_H1(smesh, 2, 0.25);
 +   }
 +
 +   SECTION("Tet")
 +   {
 +      auto smesh = DividingPlaneMesh(true, true);
-+      smesh.EnsureNCMesh();
-+      ParMesh pmesh(MPI_COMM_WORLD, smesh);
-+      test_project_H1(pmesh, 1, 0.25);
-+      test_project_H1(pmesh, 2, 0.25);
-+      test_project_H1(pmesh, 3, 0.25);
++      smesh.EnsureNCMesh(true);
++      OneSidedNCRefine(smesh);
++      test_project_H1(smesh, 3, 0.25);
 +   }
 +}
 +
- #endif // MFEM_USE_MPI
- 
- TEST_CASE("ReferenceCubeInternalBoundaries", "[NCMesh]")
++
++
+ } // namespace mfem
diff --git a/palace/CMakeLists.txt b/palace/CMakeLists.txt
index f5ad294c6..1d2d0ac6f 100644
--- a/palace/CMakeLists.txt
+++ b/palace/CMakeLists.txt
@@ -19,7 +19,7 @@ set(CMAKE_CXX_STANDARD 17)
 set(CMAKE_CXX_EXTENSIONS OFF)
 
 # Initialize the project
-project(palace LANGUAGES CXX VERSION 0.12.0)
+project(palace LANGUAGES CXX VERSION 0.13.0)
 
 # Define build settings and defaults
 set(PALACE_WITH_OPENMP OFF CACHE BOOL "Use OpenMP for shared-memory parallelism")
diff --git a/palace/models/curlcurloperator.cpp b/palace/models/curlcurloperator.cpp
index 325251ec4..42d4540a2 100644
--- a/palace/models/curlcurloperator.cpp
+++ b/palace/models/curlcurloperator.cpp
@@ -127,7 +127,7 @@ void PrintHeader(const mfem::ParFiniteElementSpace &h1_fespace,
                h1_fespace.GetMaxElementOrder(), h1_fespace.GlobalTrueVSize(),
                nd_fespace.GetMaxElementOrder(), nd_fespace.GlobalTrueVSize(),
                rt_fespace.GetMaxElementOrder(), rt_fespace.GlobalTrueVSize(),
-               (nd_fespace.GetMaxElementOrder() > BilinearForm::pa_order_threshold)
+               (nd_fespace.GetMaxElementOrder() >= BilinearForm::pa_order_threshold)
                    ? "Partial"
                    : "Full");
 
diff --git a/palace/models/laplaceoperator.cpp b/palace/models/laplaceoperator.cpp
index 833e598e6..9b3ea9d64 100644
--- a/palace/models/laplaceoperator.cpp
+++ b/palace/models/laplaceoperator.cpp
@@ -159,7 +159,7 @@ void PrintHeader(const mfem::ParFiniteElementSpace &h1_fespace,
                h1_fespace.GetMaxElementOrder(), h1_fespace.GlobalTrueVSize(),
                nd_fespace.GetMaxElementOrder(), nd_fespace.GlobalTrueVSize(),
                rt_fespace.GetMaxElementOrder(), rt_fespace.GlobalTrueVSize(),
-               (h1_fespace.GetMaxElementOrder() > BilinearForm::pa_order_threshold)
+               (h1_fespace.GetMaxElementOrder() >= BilinearForm::pa_order_threshold)
                    ? "Partial"
                    : "Full");
 
diff --git a/palace/models/spaceoperator.cpp b/palace/models/spaceoperator.cpp
index 738870a08..b15c5c70d 100644
--- a/palace/models/spaceoperator.cpp
+++ b/palace/models/spaceoperator.cpp
@@ -180,7 +180,7 @@ void PrintHeader(const mfem::ParFiniteElementSpace &h1_fespace,
                h1_fespace.GetMaxElementOrder(), h1_fespace.GlobalTrueVSize(),
                nd_fespace.GetMaxElementOrder(), nd_fespace.GlobalTrueVSize(),
                rt_fespace.GetMaxElementOrder(), rt_fespace.GlobalTrueVSize(),
-               (nd_fespace.GetMaxElementOrder() > BilinearForm::pa_order_threshold)
+               (nd_fespace.GetMaxElementOrder() >= BilinearForm::pa_order_threshold)
                    ? "Partial"
                    : "Full");
 
diff --git a/palace/models/waveportoperator.cpp b/palace/models/waveportoperator.cpp
index 4c263b9a7..e18ca8772 100644
--- a/palace/models/waveportoperator.cpp
+++ b/palace/models/waveportoperator.cpp
@@ -215,14 +215,14 @@ ComplexHypreParMatrix GetBtt(const MaterialOperator &mat_op,
 }
 
 ComplexHypreParMatrix
-GetSystemMatrixA(mfem::HypreParMatrix *Attr, mfem::HypreParMatrix *Atti,
-                 mfem::HypreParMatrix *Atnr, mfem::HypreParMatrix *Atni,
-                 mfem::HypreParMatrix *Antr, mfem::HypreParMatrix *Anti,
-                 mfem::HypreParMatrix *Annr, mfem::HypreParMatrix *Anni,
+GetSystemMatrixA(const mfem::HypreParMatrix *Attr, const mfem::HypreParMatrix *Atti,
+                 const mfem::HypreParMatrix *Atnr, const mfem::HypreParMatrix *Atni,
+                 const mfem::HypreParMatrix *Antr, const mfem::HypreParMatrix *Anti,
+                 const mfem::HypreParMatrix *Annr, const mfem::HypreParMatrix *Anni,
                  const mfem::Array<int> &dbc_tdof_list)
 {
   // Construct the 2x2 block matrices for the eigenvalue problem A e = λ B e.
-  mfem::Array2D<mfem::HypreParMatrix *> blocks(2, 2);
+  mfem::Array2D<const mfem::HypreParMatrix *> blocks(2, 2);
   blocks(0, 0) = Attr;
   blocks(0, 1) = Atnr;
   blocks(1, 0) = Antr;
@@ -250,13 +250,13 @@ GetSystemMatrixA(mfem::HypreParMatrix *Attr, mfem::HypreParMatrix *Atti,
   return {std::move(Ar), std::move(Ai)};
 }
 
-ComplexHypreParMatrix GetSystemMatrixB(mfem::HypreParMatrix *Bttr,
-                                       mfem::HypreParMatrix *Btti,
-                                       mfem::HypreParMatrix *Dnn,
+ComplexHypreParMatrix GetSystemMatrixB(const mfem::HypreParMatrix *Bttr,
+                                       const mfem::HypreParMatrix *Btti,
+                                       const mfem::HypreParMatrix *Dnn,
                                        const mfem::Array<int> &dbc_tdof_list)
 {
   // Construct the 2x2 block matrices for the eigenvalue problem A e = λ B e.
-  mfem::Array2D<mfem::HypreParMatrix *> blocks(2, 2);
+  mfem::Array2D<const mfem::HypreParMatrix *> blocks(2, 2);
   blocks(0, 0) = Bttr;
   blocks(0, 1) = nullptr;
   blocks(1, 0) = nullptr;