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Module functions

oxilean_std::finite_element_method

Module functions 

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Functionsยง

adaptive_convergence_ty
AdaptiveConvergence : FiniteElementSpace โ†’ Real โ†’ Real โ†’ Prop
affine_map_ty
AffineMap : ReferenceElement โ†’ PhysicalElement โ†’ Prop
app
app2
app3
app4
apply_dirichlet_bc
Apply Dirichlet boundary conditions by zeroing rows/columns of boundary nodes and setting the diagonal to 1 with rhs = 0.
apriori_error_estimate_ty
AprioriErrorEstimate : FiniteElementSpace โ†’ Nat โ†’ Real โ†’ Prop
arc_length_method_ty
ArcLengthMethod : BilinearForm โ†’ Real โ†’ Prop
arrow
assemble_p1_stiffness
Assemble the global P1 stiffness matrix for -ฮ”u = f on a 2D triangular mesh with homogeneous Dirichlet boundary conditions (boundary DOFs excluded).
aubin_nitsche_trick_ty
AubinNitscheTrick : Prop
bddc_preconditioner_ty
BDDCPreconditioner : FiniteElementSpace โ†’ Type
bdm_space_ty
BrezziDouglasMariniSpace : Triangulation โ†’ Nat โ†’ Type
bilinear_form_base_ty
BilinearForm : Type (base declaration for a: Vร—V โ†’ โ„)
bool_ty
brezzi_splitting_ty
BrezziSplitting : MixedFEProblem โ†’ Prop
bspline_basis_ty
BSplineBasis : Nat โ†’ Nat โ†’ Type
bubnov_galerkin_consistency_ty
BubnovGalerkinConsistency : BilinearForm โ†’ FiniteElementSpace โ†’ Prop
build_fem_env
build_fem_env_extended
Register all new FEM axioms (Sections 11-20) into env.
bvar
cea_lemma_ty
CeaLemma : โˆ€ (a : BilinearForm) (ฮฑ M : Real) (Vh : FESpace) (u uh : H1), IsCoercive a ฮฑ โ†’ IsBounded a M โ†’ GalerkinSolution a f Vh uh โ†’ โ€–u - uhโ€–_V โ‰ค (M/ฮฑ) * inf_{vh โˆˆ Vh} โ€–u - vhโ€–_V
conjugate_gradient
Solve A x = b using the conjugate gradient method. Assumes A is symmetric positive definite.
consistent_linearization_ty
ConsistentLinearization : BilinearForm โ†’ H1Space โ†’ BilinearForm
cst
de_rham_complex_ty
DeRhamComplex : Triangulation โ†’ Prop
dg_coercivity_ty
DGCoercivity : InteriorPenaltyForm โ†’ Real โ†’ Prop
dg_consistency_ty
DGConsistency : InteriorPenaltyForm โ†’ Prop
dg_error_estimate_ty
DGErrorEstimate : DGSpace โ†’ Nat โ†’ Real โ†’ Prop
dg_space_ty
DGSpace : Triangulation โ†’ Nat โ†’ Type
dist
domain_decomposition_ty
DomainDecompositionMethod : FiniteElementSpace โ†’ Nat โ†’ Prop
dorfler_marking_ty
DorflerMarking : ResidualEstimator โ†’ Real โ†’ Subset โ†’ Prop
dot
efficiency_bound_ty
EfficiencyBound : ResidualEstimator โ†’ Prop
element_residuals_1d
Compute element residual error indicators for a 1D P1 FEM solution of -uโ€™โ€™ = f.
exponential_convergence_ty
ExponentialConvergence : FiniteElementSpace โ†’ Real โ†’ Prop
fem_well_posedness_ty
FEMWellPosedness : BilinearForm โ†’ LinearForm โ†’ FiniteElementSpace โ†’ Prop
feti_preconditioner_ty
FETIPreconditioner : FiniteElementSpace โ†’ Type
finite_element_space_ty
FiniteElementSpace : Type (base declaration)
fluid_structure_interaction_ty
FluidStructureInteraction : BilinearForm โ†’ BilinearForm โ†’ Prop
fn_ty
galerkin_orthogonality_ty
GalerkinOrthogonality : BilinearForm โ†’ H1Space โ†’ FiniteElementSpace โ†’ Prop
galerkin_problem_ty
GalerkinProblem : BilinearForm โ†’ LinearForm โ†’ FiniteElementSpace โ†’ Prop
global_error_estimator
Global a posteriori error bound: ฮท = (ฮฃ_i ฮท_iยฒ)^{1/2}.
goal_oriented_estimator_ty
GoalOrientedEstimator : FiniteElementSpace โ†’ LinearForm โ†’ Real
h_refinement_ty
HRefinement : Triangulation โ†’ Triangulation โ†’ Prop
hcurl_conforming_ty
HCurlConforming : FiniteElementSpace โ†’ Prop
hdiv_conforming_ty
HDivConforming : FiniteElementSpace โ†’ Prop
hp_adaptivity_ty
HPAdaptivity : Triangulation โ†’ FiniteElementSpace โ†’ Prop
inf_sup_condition_ty
InfSupCondition : BilinearForm โ†’ Real โ†’ Prop
interior_penalty_form_ty
InteriorPenaltyForm : DGSpace โ†’ Real โ†’ BilinearForm
interpolation_error_ty
InterpolationError : FiniteElementSpace โ†’ Nat โ†’ Real โ†’ Prop
interpolation_operator_ty
InterpolationOperator : H1Space โ†’ FiniteElementSpace โ†’ H1Space
is_bounded_ty
IsBounded : BilinearForm โ†’ Real โ†’ Prop
is_coercive_ty
IsCoercive : BilinearForm โ†’ Real โ†’ Prop
is_conforming_ty
IsConforming : Triangulation โ†’ Prop
is_quasiuniform_ty
IsQuasiuniform : Triangulation โ†’ Real โ†’ Prop
is_shape_regular_ty
IsShapeRegular : Triangulation โ†’ Real โ†’ Prop
is_subspace_ty
IsSubspace : FiniteElementSpace โ†’ H1Space โ†’ Prop
isogeometric_convergence_ty
IsogeometricConvergence : IsogeometricSpace โ†’ Nat โ†’ Real โ†’ Prop
isogeometric_space_ty
IsogeometricSpace : NURBSSurface โ†’ Nat โ†’ Type
jacobian_determinant_ty
JacobianDeterminant : AffineMap โ†’ Real
kirchhoff_love_plate_ty
KirchhoffLovePlate : Triangulation โ†’ Nat โ†’ Type
l2_error_estimate_ty
L2ErrorEstimate : FiniteElementSpace โ†’ Nat โ†’ Real โ†’ Prop
lagrange_p1_space_ty
LagrangeP1Space : Triangulation โ†’ FiniteElementSpace
lagrange_p2_space_ty
LagrangeP2Space : Triangulation โ†’ FiniteElementSpace
lax_milgram_discrete_ty
LaxMilgramDiscrete : โˆ€ (a : BilinearForm) (f : LinearForm) (Vh : FESpace), IsCoercive a โ†’ IsBounded a โ†’ โˆƒ! uh : H1Space, GalerkinSolution a f Vh uh
linear_form_ty
LinearForm : Type (rhs functional f : V โ†’ โ„)
mass_matrix_ty
MassMatrix : FiniteElementSpace โ†’ Matrix
mesh_size_ty
MeshSize : Triangulation โ†’ Real
mesh_vertex_ty
MeshVertex : Type
mini_element_ty
MiniElement : Triangulation โ†’ FiniteElementSpace
mixed_fe_problem_ty
MixedFEProblem : BilinearForm โ†’ BilinearForm โ†’ LinearForm โ†’ LinearForm โ†’ Prop
mixed_fem_error_estimate_ty
MixedFEMErrorEstimate : BilinearForm โ†’ BilinearForm โ†’ FiniteElementSpace โ†’ Prop
multigrid_optimality_ty
MultigridOptimality : MultigridPreconditioner โ†’ Prop
multigrid_preconditioner_ty
MultigridPreconditioner : FiniteElementSpace โ†’ Type
nat_ty
nedelec_space_ty
NedelecSpace : Triangulation โ†’ Nat โ†’ Type
newton_raphson_fem_ty
NewtonRaphsonFEM : BilinearForm โ†’ LinearForm โ†’ FiniteElementSpace โ†’ Prop
nitsche_bilinear_form_ty
NitscheBilinearForm : BilinearForm โ†’ Real โ†’ BilinearForm
nitsche_coercivity_ty
NitscheCoercivity : NitscheBilinearForm โ†’ Real โ†’ Prop
nitsche_consistency_ty
NitscheConsistency : NitscheBilinearForm โ†’ Prop
nitsche_optimal_convergence_ty
NitscheOptimalConvergence : FiniteElementSpace โ†’ Nat โ†’ Prop
num_dof_ty
NumDOF : FiniteElementSpace โ†’ Nat
num_elements_ty
NumElements : Triangulation โ†’ Nat
nurbs_surface_ty
NURBSSurface : BSplineBasis โ†’ BSplineBasis โ†’ Type
operator_splitting_ty
OperatorSplitting : CoupledProblem โ†’ Prop
p1_grad
Gradient of P1 shape functions on the reference triangle (constant).
p1_shape
The three Lagrange P1 shape functions on the reference triangle Kฬ‚.
p2_shape
Evaluate the six Lagrange P2 shape functions on the reference triangle.
p_refinement_ty
PRefinement : FiniteElementSpace โ†’ Nat โ†’ FiniteElementSpace โ†’ Prop
parabolic_stability_ty
ParabolicStability : SpaceTimeFESpace โ†’ Prop
petrov_galerkin_problem_ty
PetrovGalerkinProblem : BilinearForm โ†’ LinearForm โ†’ FESpace โ†’ FESpace โ†’ Prop
pi
poro_elasticity_biot_ty
PoroElasticityBiot : BilinearForm โ†’ BilinearForm โ†’ Prop
prop
quadratic_convergence_newton_ty
QuadraticConvergenceNewton : NewtonRaphsonFEM โ†’ Prop
raviart_thomas_space_ty
RaviartThomasSpace : Triangulation โ†’ Nat โ†’ Type
real_ty
reduced_integration_ty
ReducedIntegration : FiniteElementSpace โ†’ Nat โ†’ Prop
reference_hexahedron_ty
ReferenceHexahedron : Type
reference_tetrahedron_ty
ReferenceTetrahedron : Type
reference_triangle_quadrature
3-point quadrature rule on the reference triangle (degree 2 exact).
reference_triangle_ty
ReferenceTriangle : Type
reissner_mindlin_plate_ty
ReissnerMindlinPlate : Triangulation โ†’ Nat โ†’ Type
reliability_bound_ty
ReliabilityBound : ResidualEstimator โ†’ Prop
residual_estimator_ty
ResidualEstimator : FiniteElementSpace โ†’ H1Space โ†’ Real
shape_function_gradient_ty
ShapeFunctionGradient : ReferenceTriangle โ†’ Nat โ†’ (Real โ†’ Real โ†’ Real ร— Real)
shape_function_ty
ShapeFunction : ReferenceTriangle โ†’ Nat โ†’ (Real โ†’ Real โ†’ Real)
shear_locking_freedom_ty
ShearLockingFreedom : ReissnerMindlinPlate โ†’ Prop
space_time_error_estimate_ty
SpaceTimeErrorEstimate : SpaceTimeFESpace โ†’ Nat โ†’ Real โ†’ Prop
space_time_fe_space_ty
SpaceTimeFESpace : FiniteElementSpace โ†’ Real โ†’ Type
stability_estimate_ty
StabilityEstimate : BilinearForm โ†’ LinearForm โ†’ Prop
stiffness_matrix_ty
StiffnessMatrix : FiniteElementSpace โ†’ Matrix
taylor_hood_element_ty
TaylorHoodElement : Triangulation โ†’ FiniteElementSpace
thermo_mechanical_coupling_ty
ThermoMechanicalCoupling : BilinearForm โ†’ BilinearForm โ†’ LinearForm โ†’ Prop
triangulation_element_ty
TriangulationElement : Type
triangulation_ty
Triangulation : Nat โ†’ Type
tspline_space_ty
TSplineSpace : Nat โ†’ Type
type0
upg_form_ty
UPGForm : DGSpace โ†’ Real โ†’ BilinearForm
wave_energy_conservation_ty
WaveEnergyConservation : SpaceTimeFESpace โ†’ Prop
zz_estimator_ty
ZZEstimator : FiniteElementSpace โ†’ H1Space โ†’ Real