diff --git a/examples/advect-eqn/test/CMakeLists.txt b/examples/advect-eqn/test/CMakeLists.txt
index 11dbcaee..09796dcc 100644
--- a/examples/advect-eqn/test/CMakeLists.txt
+++ b/examples/advect-eqn/test/CMakeLists.txt
@@ -1,5 +1,7 @@
 include(TesterExodusII)
 
+if(${PETSC_VERSION} VERSION_LESS "3.21.0")
+
 add_test_exodiff(
     NAME   advect
     BIN    ${PROJECT_NAME}
@@ -8,3 +10,5 @@ add_test_exodiff(
     GOLD   ${PROJECT_SOURCE_DIR}/test/gold/1d.exo
     ARGS   -Floor 1e-16
 )
+
+endif()
\ No newline at end of file
diff --git a/src/FVProblemInterface.cpp b/src/FVProblemInterface.cpp
index 3b57d582..11488668 100644
--- a/src/FVProblemInterface.cpp
+++ b/src/FVProblemInterface.cpp
@@ -367,6 +367,11 @@ FVProblemInterface::create()
     DiscreteProblemInterface::create();
     get_unstr_mesh()->construct_ghost_cells();
     get_unstr_mesh()->localize_coordinates();
+
+#if PETSC_VERSION_GE(3, 21, 0)
+    if (get_unstr_mesh()->get_dimension() == 1)
+        throw Exception("FV in 1D is not possible due to a bug in PETSc. Use PETSc 3.20 instead.");
+#endif
 }
 
 void
diff --git a/test/src/ExplicitFVLinearProblem_test.cpp b/test/src/ExplicitFVLinearProblem_test.cpp
index d19113da..c66c2189 100644
--- a/test/src/ExplicitFVLinearProblem_test.cpp
+++ b/test/src/ExplicitFVLinearProblem_test.cpp
@@ -1,6 +1,7 @@
 #include "gmock/gmock.h"
 #include "godzilla/CallStack.h"
 #include "godzilla/LineMesh.h"
+#include "godzilla/RectangleMesh.h"
 #include "godzilla/NaturalRiemannBC.h"
 #include "godzilla/ExplicitFVLinearProblem.h"
 #include "godzilla/Parameters.h"
@@ -112,10 +113,19 @@ TEST(ExplicitFVLinearProblemTest, api)
 {
     TestApp app;
 
+#if PETSC_VERSION_GE(3, 21, 0)
+    // PETSc 3.21.0+ has a bug in forming the mass matrix in 1D, se we use 2D mesh in this test
+    Parameters mesh_pars = RectangleMesh::parameters();
+    mesh_pars.set<App *>("_app") = &app;
+    mesh_pars.set<Int>("nx") = 2;
+    mesh_pars.set<Int>("ny") = 1;
+    RectangleMesh mesh(mesh_pars);
+#else
     Parameters mesh_pars = LineMesh::parameters();
     mesh_pars.set<App *>("_app") = &app;
     mesh_pars.set<Int>("nx") = 2;
     LineMesh mesh(mesh_pars);
+#endif
 
     Parameters prob_pars = TestExplicitFVLinearProblem::parameters();
     prob_pars.set<App *>("_app") = &app;
@@ -201,10 +211,19 @@ TEST(ExplicitFVLinearProblemTest, fields)
 {
     TestApp app;
 
+#if PETSC_VERSION_GE(3, 21, 0)
+    // PETSc 3.21.0+ has a bug in forming the mass matrix in 1D, se we use 2D mesh in this test
+    Parameters mesh_pars = RectangleMesh::parameters();
+    mesh_pars.set<App *>("_app") = &app;
+    mesh_pars.set<Int>("nx") = 2;
+    mesh_pars.set<Int>("ny") = 1;
+    RectangleMesh mesh(mesh_pars);
+#else
     Parameters mesh_pars = LineMesh::parameters();
     mesh_pars.set<App *>("_app") = &app;
     mesh_pars.set<Int>("nx") = 2;
     LineMesh mesh(mesh_pars);
+#endif
 
     Parameters prob_pars = TestExplicitFVLinearProblem::parameters();
     prob_pars.set<App *>("_app") = &app;
@@ -244,10 +263,20 @@ TEST(ExplicitFVLinearProblemTest, test_mass_matrix)
 {
     TestApp app;
 
+#if PETSC_VERSION_GE(3, 21, 0)
+    // PETSc 3.21.0+ has a bug in forming the mass matrix in 1D, se we use 2D mesh in this test
+    Parameters mesh_pars = RectangleMesh::parameters();
+    mesh_pars.set<App *>("_app") = &app;
+    mesh_pars.set<Int>("nx") = 3;
+    mesh_pars.set<Int>("ny") = 1;
+    mesh_pars.set<Real>("ymax") = 3.;
+    RectangleMesh mesh(mesh_pars);
+#else
     Parameters mesh_pars = LineMesh::parameters();
     mesh_pars.set<App *>("_app") = &app;
     mesh_pars.set<Int>("nx") = 3;
     LineMesh mesh(mesh_pars);
+#endif
 
     Parameters prob_pars = TestExplicitFVLinearProblem::parameters();
     prob_pars.set<App *>("_app") = &app;
@@ -276,6 +305,9 @@ TEST(ExplicitFVLinearProblemTest, solve)
 {
     TestApp app;
 
+#if PETSC_VERSION_GE(3, 21, 0)
+    // PETSc 3.21.0+ has a bug in forming the mass matrix in 1D, se we use 2D mesh in this test
+#else
     Parameters mesh_pars = LineMesh::parameters();
     mesh_pars.set<App *>("_app") = &app;
     mesh_pars.set<Int>("nx") = 2;
@@ -330,16 +362,26 @@ TEST(ExplicitFVLinearProblemTest, solve)
     EXPECT_NEAR(lx[2], 0., 1e-15);
     EXPECT_NEAR(lx[3], 0., 1e-15);
     loc_sln.restore_array_read(lx);
+#endif
 }
 
 TEST(ExplicitFVLinearProblemTest, set_schemes)
 {
     TestApp app;
 
+#if PETSC_VERSION_GE(3, 21, 0)
+    // PETSc 3.21.0+ has a bug in forming the mass matrix in 1D, se we use 2D mesh in this test
+    Parameters mesh_pars = RectangleMesh::parameters();
+    mesh_pars.set<App *>("_app") = &app;
+    mesh_pars.set<Int>("nx") = 2;
+    mesh_pars.set<Int>("ny") = 1;
+    RectangleMesh mesh(mesh_pars);
+#else
     Parameters mesh_pars = LineMesh::parameters();
     mesh_pars.set<App *>("_app") = &app;
     mesh_pars.set<Int>("nx") = 2;
     LineMesh mesh(mesh_pars);
+#endif
 
     Parameters prob_pars = TestExplicitFVLinearProblem::parameters();
     prob_pars.set<App *>("_app") = &app;
@@ -373,10 +415,19 @@ TEST(ExplicitFVLinearProblemTest, wrong_schemes)
 
     TestApp app;
 
+#if PETSC_VERSION_GE(3, 21, 0)
+    // PETSc 3.21.0+ has a bug in forming the mass matrix in 1D, se we use 2D mesh in this test
+    Parameters mesh_pars = RectangleMesh::parameters();
+    mesh_pars.set<App *>("_app") = &app;
+    mesh_pars.set<Int>("nx") = 2;
+    mesh_pars.set<Int>("ny") = 1;
+    RectangleMesh mesh(mesh_pars);
+#else
     Parameters mesh_pars = LineMesh::parameters();
     mesh_pars.set<App *>("_app") = &app;
     mesh_pars.set<Int>("nx") = 2;
     LineMesh mesh(mesh_pars);
+#endif
 
     Parameters prob_pars = TestExplicitFVLinearProblem::parameters();
     prob_pars.set<App *>("_app") = &app;