+
+
Link to the source code for this example:
+
Open vector_fe_ex6 in new tab.
+
+
The console output of the program:
+
+***************************************************************
+* Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=TRI6 boundary_condition=neumann
+***************************************************************
+
+ Mesh Information:
+ elem_dimensions()={2}
+ spatial_dimension()=2
+ n_nodes()=961
+ n_local_nodes()=961
+ n_elem()=450
+ n_local_elem()=450
+ n_active_elem()=450
+ n_subdomains()=1
+ n_elemsets()=0
+ n_partitions()=1
+ n_processors()=1
+ n_threads()=1
+ processor_id()=0
+ is_prepared()=true
+ is_replicated()=true
+
+ EquationSystems
+ n_systems()=1
+ System #0, "DivGrad"
+ Type "LinearImplicit"
+ Variables="u" "p" "l"
+ Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
+ Approximation Orders="FIRST" "CONSTANT" "FIRST"
+ n_dofs()=1156
+ n_local_dofs()=1156
+ max(n_local_dofs())=1156
+ n_constrained_dofs()=0
+ n_local_constrained_dofs()=0
+ max(local unconstrained dofs)=1156
+ n_vectors()=1
+ n_matrices()=1
+ DofMap Sparsity
+ Average On-Processor Bandwidth <= 7.66955
+ Average Off-Processor Bandwidth <= 0
+ Maximum On-Processor Bandwidth <= 1156
+ Maximum Off-Processor Bandwidth <= 0
+ DofMap Constraints
+ Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.134373
+HDiv semi-norm error is: 0.344042
+HDiv error is: 0.369353
+~~ Scalar field (p) ~~
+L2 error is: 0.0697862
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=TRI6 boundary_condition=neumann
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=TRI7 boundary_condition=neumann
+***************************************************************
+
+ Mesh Information:
+ elem_dimensions()={2}
+ spatial_dimension()=2
+ n_nodes()=1411
+ n_local_nodes()=1411
+ n_elem()=450
+ n_local_elem()=450
+ n_active_elem()=450
+ n_subdomains()=1
+ n_elemsets()=0
+ n_partitions()=1
+ n_processors()=1
+ n_threads()=1
+ processor_id()=0
+ is_prepared()=true
+ is_replicated()=true
+
+ EquationSystems
+ n_systems()=1
+ System #0, "DivGrad"
+ Type "LinearImplicit"
+ Variables="u" "p" "l"
+ Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
+ Approximation Orders="FIRST" "CONSTANT" "FIRST"
+ n_dofs()=1156
+ n_local_dofs()=1156
+ max(n_local_dofs())=1156
+ n_constrained_dofs()=0
+ n_local_constrained_dofs()=0
+ max(local unconstrained dofs)=1156
+ n_vectors()=1
+ n_matrices()=1
+ DofMap Sparsity
+ Average On-Processor Bandwidth <= 7.66955
+ Average Off-Processor Bandwidth <= 0
+ Maximum On-Processor Bandwidth <= 1156
+ Maximum Off-Processor Bandwidth <= 0
+ DofMap Constraints
+ Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.134373
+HDiv semi-norm error is: 0.344042
+HDiv error is: 0.369353
+~~ Scalar field (p) ~~
+L2 error is: 0.0697862
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=TRI7 boundary_condition=neumann
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=QUAD8 boundary_condition=neumann
+***************************************************************
+
+ Mesh Information:
+ elem_dimensions()={2}
+ spatial_dimension()=2
+ n_nodes()=736
+ n_local_nodes()=736
+ n_elem()=225
+ n_local_elem()=225
+ n_active_elem()=225
+ n_subdomains()=1
+ n_elemsets()=0
+ n_partitions()=1
+ n_processors()=1
+ n_threads()=1
+ processor_id()=0
+ is_prepared()=true
+ is_replicated()=true
+
+ EquationSystems
+ n_systems()=1
+ System #0, "DivGrad"
+ Type "LinearImplicit"
+ Variables="u" "p" "l"
+ Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
+ Approximation Orders="FIRST" "CONSTANT" "FIRST"
+ n_dofs()=706
+ n_local_dofs()=706
+ max(n_local_dofs())=706
+ n_constrained_dofs()=0
+ n_local_constrained_dofs()=0
+ max(local unconstrained dofs)=706
+ n_vectors()=1
+ n_matrices()=1
+ DofMap Sparsity
+ Average On-Processor Bandwidth <= 9.3711
+ Average Off-Processor Bandwidth <= 0
+ Maximum On-Processor Bandwidth <= 706
+ Maximum Off-Processor Bandwidth <= 0
+ DofMap Constraints
+ Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.134503
+HDiv semi-norm error is: 0.421249
+HDiv error is: 0.442201
+~~ Scalar field (p) ~~
+L2 error is: 0.0854505
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=QUAD8 boundary_condition=neumann
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=QUAD9 boundary_condition=neumann
+***************************************************************
+
+ Mesh Information:
+ elem_dimensions()={2}
+ spatial_dimension()=2
+ n_nodes()=961
+ n_local_nodes()=961
+ n_elem()=225
+ n_local_elem()=225
+ n_active_elem()=225
+ n_subdomains()=1
+ n_elemsets()=0
+ n_partitions()=1
+ n_processors()=1
+ n_threads()=1
+ processor_id()=0
+ is_prepared()=true
+ is_replicated()=true
+
+ EquationSystems
+ n_systems()=1
+ System #0, "DivGrad"
+ Type "LinearImplicit"
+ Variables="u" "p" "l"
+ Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
+ Approximation Orders="FIRST" "CONSTANT" "FIRST"
+ n_dofs()=706
+ n_local_dofs()=706
+ max(n_local_dofs())=706
+ n_constrained_dofs()=0
+ n_local_constrained_dofs()=0
+ max(local unconstrained dofs)=706
+ n_vectors()=1
+ n_matrices()=1
+ DofMap Sparsity
+ Average On-Processor Bandwidth <= 9.3711
+ Average Off-Processor Bandwidth <= 0
+ Maximum On-Processor Bandwidth <= 706
+ Maximum Off-Processor Bandwidth <= 0
+ DofMap Constraints
+ Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.134503
+HDiv semi-norm error is: 0.421249
+HDiv error is: 0.442201
+~~ Scalar field (p) ~~
+L2 error is: 0.0854505
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=QUAD9 boundary_condition=neumann
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+* ./example-opt dim=3 element_type=TET14 grid_size=6 boundary_condition=neumann
+***************************************************************
+
+ Mesh Information:
+ elem_dimensions()={3}
+ spatial_dimension()=3
+ n_nodes()=19045
+ n_local_nodes()=19045
+ n_elem()=5184
+ n_local_elem()=5184
+ n_active_elem()=5184
+ n_subdomains()=1
+ n_elemsets()=0
+ n_partitions()=1
+ n_processors()=1
+ n_threads()=1
+ processor_id()=0
+ is_prepared()=true
+ is_replicated()=true
+
+ EquationSystems
+ n_systems()=1
+ System #0, "DivGrad"
+ Type "LinearImplicit"
+ Variables="u" "p" "l"
+ Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
+ Approximation Orders="FIRST" "CONSTANT" "FIRST"
+ n_dofs()=15985
+ n_local_dofs()=15985
+ max(n_local_dofs())=15985
+ n_constrained_dofs()=0
+ n_local_constrained_dofs()=0
+ max(local unconstrained dofs)=15985
+ n_vectors()=1
+ n_matrices()=1
+ DofMap Sparsity
+ Average On-Processor Bandwidth <= 9.48596
+ Average Off-Processor Bandwidth <= 0
+ Maximum On-Processor Bandwidth <= 15985
+ Maximum Off-Processor Bandwidth <= 0
+ DofMap Constraints
+ Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.334771
+HDiv semi-norm error is: 0.836328
+HDiv error is: 0.900842
+~~ Scalar field (p) ~~
+L2 error is: 0.113127
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+* ./example-opt dim=3 element_type=TET14 grid_size=6 boundary_condition=neumann
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+* ./example-opt dim=3 element_type=HEX27 boundary_condition=neumann
+***************************************************************
+
+ Mesh Information:
+ elem_dimensions()={3}
+ spatial_dimension()=3
+ n_nodes()=29791
+ n_local_nodes()=29791
+ n_elem()=3375
+ n_local_elem()=3375
+ n_active_elem()=3375
+ n_subdomains()=1
+ n_elemsets()=0
+ n_partitions()=1
+ n_processors()=1
+ n_threads()=1
+ processor_id()=0
+ is_prepared()=true
+ is_replicated()=true
+
+ EquationSystems
+ n_systems()=1
+ System #0, "DivGrad"
+ Type "LinearImplicit"
+ Variables="u" "p" "l"
+ Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
+ Approximation Orders="FIRST" "CONSTANT" "FIRST"
+ n_dofs()=14176
+ n_local_dofs()=14176
+ max(n_local_dofs())=14176
+ n_constrained_dofs()=0
+ n_local_constrained_dofs()=0
+ max(local unconstrained dofs)=14176
+ n_vectors()=1
+ n_matrices()=1
+ DofMap Sparsity
+ Average On-Processor Bandwidth <= 12.9992
+ Average Off-Processor Bandwidth <= 0
+ Maximum On-Processor Bandwidth <= 14176
+ Maximum Off-Processor Bandwidth <= 0
+ DofMap Constraints
+ Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.2325
+HDiv semi-norm error is: 0.773177
+HDiv error is: 0.807378
+~~ Scalar field (p) ~~
+L2 error is: 0.104528
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+* ./example-opt dim=3 element_type=HEX27 boundary_condition=neumann
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=TRI6 boundary_condition=dirichlet
+***************************************************************
+
+ Mesh Information:
+ elem_dimensions()={2}
+ spatial_dimension()=2
+ n_nodes()=961
+ n_local_nodes()=961
+ n_elem()=450
+ n_local_elem()=450
+ n_active_elem()=450
+ n_subdomains()=1
+ n_elemsets()=0
+ n_partitions()=1
+ n_processors()=1
+ n_threads()=1
+ processor_id()=0
+ is_prepared()=true
+ is_replicated()=true
+
+ EquationSystems
+ n_systems()=1
+ System #0, "DivGrad"
+ Type "LinearImplicit"
+ Variables="u" "p"
+ Finite Element Types="RAVIART_THOMAS" "MONOMIAL"
+ Approximation Orders="FIRST" "CONSTANT"
+ n_dofs()=1155
+ n_local_dofs()=1155
+ max(n_local_dofs())=1155
+ n_constrained_dofs()=0
+ n_local_constrained_dofs()=0
+ max(local unconstrained dofs)=1155
+ n_vectors()=1
+ n_matrices()=1
+ DofMap Sparsity
+ Average On-Processor Bandwidth <= 5.67532
+ Average Off-Processor Bandwidth <= 0
+ Maximum On-Processor Bandwidth <= 7
+ Maximum Off-Processor Bandwidth <= 0
+ DofMap Constraints
+ Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.134279
+HDiv semi-norm error is: 0.344042
+HDiv error is: 0.369318
+~~ Scalar field (p) ~~
+L2 error is: 0.0697398
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=TRI6 boundary_condition=dirichlet
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=TRI7 boundary_condition=dirichlet
+***************************************************************
+
+ Mesh Information:
+ elem_dimensions()={2}
+ spatial_dimension()=2
+ n_nodes()=1411
+ n_local_nodes()=1411
+ n_elem()=450
+ n_local_elem()=450
+ n_active_elem()=450
+ n_subdomains()=1
+ n_elemsets()=0
+ n_partitions()=1
+ n_processors()=1
+ n_threads()=1
+ processor_id()=0
+ is_prepared()=true
+ is_replicated()=true
+
+ EquationSystems
+ n_systems()=1
+ System #0, "DivGrad"
+ Type "LinearImplicit"
+ Variables="u" "p"
+ Finite Element Types="RAVIART_THOMAS" "MONOMIAL"
+ Approximation Orders="FIRST" "CONSTANT"
+ n_dofs()=1155
+ n_local_dofs()=1155
+ max(n_local_dofs())=1155
+ n_constrained_dofs()=0
+ n_local_constrained_dofs()=0
+ max(local unconstrained dofs)=1155
+ n_vectors()=1
+ n_matrices()=1
+ DofMap Sparsity
+ Average On-Processor Bandwidth <= 5.67532
+ Average Off-Processor Bandwidth <= 0
+ Maximum On-Processor Bandwidth <= 7
+ Maximum Off-Processor Bandwidth <= 0
+ DofMap Constraints
+ Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.134279
+HDiv semi-norm error is: 0.344042
+HDiv error is: 0.369318
+~~ Scalar field (p) ~~
+L2 error is: 0.0697398
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=TRI7 boundary_condition=dirichlet
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=QUAD8 boundary_condition=dirichlet
+***************************************************************
+
+ Mesh Information:
+ elem_dimensions()={2}
+ spatial_dimension()=2
+ n_nodes()=736
+ n_local_nodes()=736
+ n_elem()=225
+ n_local_elem()=225
+ n_active_elem()=225
+ n_subdomains()=1
+ n_elemsets()=0
+ n_partitions()=1
+ n_processors()=1
+ n_threads()=1
+ processor_id()=0
+ is_prepared()=true
+ is_replicated()=true
+
+ EquationSystems
+ n_systems()=1
+ System #0, "DivGrad"
+ Type "LinearImplicit"
+ Variables="u" "p"
+ Finite Element Types="RAVIART_THOMAS" "MONOMIAL"
+ Approximation Orders="FIRST" "CONSTANT"
+ n_dofs()=705
+ n_local_dofs()=705
+ max(n_local_dofs())=705
+ n_constrained_dofs()=0
+ n_local_constrained_dofs()=0
+ max(local unconstrained dofs)=705
+ n_vectors()=1
+ n_matrices()=1
+ DofMap Sparsity
+ Average On-Processor Bandwidth <= 7.38298
+ Average Off-Processor Bandwidth <= 0
+ Maximum On-Processor Bandwidth <= 9
+ Maximum Off-Processor Bandwidth <= 0
+ DofMap Constraints
+ Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.134333
+HDiv semi-norm error is: 0.421249
+HDiv error is: 0.442149
+~~ Scalar field (p) ~~
+L2 error is: 0.0853821
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=QUAD8 boundary_condition=dirichlet
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=QUAD9 boundary_condition=dirichlet
+***************************************************************
+
+ Mesh Information:
+ elem_dimensions()={2}
+ spatial_dimension()=2
+ n_nodes()=961
+ n_local_nodes()=961
+ n_elem()=225
+ n_local_elem()=225
+ n_active_elem()=225
+ n_subdomains()=1
+ n_elemsets()=0
+ n_partitions()=1
+ n_processors()=1
+ n_threads()=1
+ processor_id()=0
+ is_prepared()=true
+ is_replicated()=true
+
+ EquationSystems
+ n_systems()=1
+ System #0, "DivGrad"
+ Type "LinearImplicit"
+ Variables="u" "p"
+ Finite Element Types="RAVIART_THOMAS" "MONOMIAL"
+ Approximation Orders="FIRST" "CONSTANT"
+ n_dofs()=705
+ n_local_dofs()=705
+ max(n_local_dofs())=705
+ n_constrained_dofs()=0
+ n_local_constrained_dofs()=0
+ max(local unconstrained dofs)=705
+ n_vectors()=1
+ n_matrices()=1
+ DofMap Sparsity
+ Average On-Processor Bandwidth <= 7.38298
+ Average Off-Processor Bandwidth <= 0
+ Maximum On-Processor Bandwidth <= 9
+ Maximum Off-Processor Bandwidth <= 0
+ DofMap Constraints
+ Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.134333
+HDiv semi-norm error is: 0.421249
+HDiv error is: 0.442149
+~~ Scalar field (p) ~~
+L2 error is: 0.0853821
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=QUAD9 boundary_condition=dirichlet
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+* ./example-opt dim=3 element_type=TET14 grid_size=6 boundary_condition=dirichlet
+***************************************************************
+
+ Mesh Information:
+ elem_dimensions()={3}
+ spatial_dimension()=3
+ n_nodes()=19045
+ n_local_nodes()=19045
+ n_elem()=5184
+ n_local_elem()=5184
+ n_active_elem()=5184
+ n_subdomains()=1
+ n_elemsets()=0
+ n_partitions()=1
+ n_processors()=1
+ n_threads()=1
+ processor_id()=0
+ is_prepared()=true
+ is_replicated()=true
+
+ EquationSystems
+ n_systems()=1
+ System #0, "DivGrad"
+ Type "LinearImplicit"
+ Variables="u" "p"
+ Finite Element Types="RAVIART_THOMAS" "MONOMIAL"
+ Approximation Orders="FIRST" "CONSTANT"
+ n_dofs()=15984
+ n_local_dofs()=15984
+ max(n_local_dofs())=15984
+ n_constrained_dofs()=0
+ n_local_constrained_dofs()=0
+ max(local unconstrained dofs)=15984
+ n_vectors()=1
+ n_matrices()=1
+ DofMap Sparsity
+ Average On-Processor Bandwidth <= 7.48649
+ Average Off-Processor Bandwidth <= 0
+ Maximum On-Processor Bandwidth <= 9
+ Maximum Off-Processor Bandwidth <= 0
+ DofMap Constraints
+ Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.33473
+HDiv semi-norm error is: 0.836328
+HDiv error is: 0.900826
+~~ Scalar field (p) ~~
+L2 error is: 0.113105
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+* ./example-opt dim=3 element_type=TET14 grid_size=6 boundary_condition=dirichlet
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+* ./example-opt dim=3 element_type=HEX27 boundary_condition=dirichlet
+***************************************************************
+
+ Mesh Information:
+ elem_dimensions()={3}
+ spatial_dimension()=3
+ n_nodes()=29791
+ n_local_nodes()=29791
+ n_elem()=3375
+ n_local_elem()=3375
+ n_active_elem()=3375
+ n_subdomains()=1
+ n_elemsets()=0
+ n_partitions()=1
+ n_processors()=1
+ n_threads()=1
+ processor_id()=0
+ is_prepared()=true
+ is_replicated()=true
+
+ EquationSystems
+ n_systems()=1
+ System #0, "DivGrad"
+ Type "LinearImplicit"
+ Variables="u" "p"
+ Finite Element Types="RAVIART_THOMAS" "MONOMIAL"
+ Approximation Orders="FIRST" "CONSTANT"
+ n_dofs()=14175
+ n_local_dofs()=14175
+ max(n_local_dofs())=14175
+ n_constrained_dofs()=0
+ n_local_constrained_dofs()=0
+ max(local unconstrained dofs)=14175
+ n_vectors()=1
+ n_matrices()=1
+ DofMap Sparsity
+ Average On-Processor Bandwidth <= 11
+ Average Off-Processor Bandwidth <= 0
+ Maximum On-Processor Bandwidth <= 13
+ Maximum Off-Processor Bandwidth <= 0
+ DofMap Constraints
+ Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.23237
+HDiv semi-norm error is: 0.773177
+HDiv error is: 0.807341
+~~ Scalar field (p) ~~
+L2 error is: 0.104476
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+* ./example-opt dim=3 element_type=HEX27 boundary_condition=dirichlet
+***************************************************************
+
+