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
***************************************************************