ErrorControl.h

Note

The documentation on this page was automatically extracted from the DOLFIN C++ code and may need to be edited or expanded.

class ErrorControl

Parent class(es)

• Hierarchical
• Variable

(Goal-oriented) Error Control class. The notation used here follows the notation in “Automated goal-oriented error control I: stationary variational problems”, ME Rognes and A Logg, 2010-2011.

ErrorControl(std::shared_ptr<Form> a_star, std::shared_ptr<Form> L_star, std::shared_ptr<Form> residual, std::shared_ptr<Form> a_R_T, std::shared_ptr<Form> L_R_T, std::shared_ptr<Form> a_R_dT, std::shared_ptr<Form> L_R_dT, std::shared_ptr<Form> eta_T, bool is_linear)

Create error control object

Arguments

a_star (Form)

the bilinear form for the dual problem

L_star (Form)

the linear form for the dual problem

residual (Form)

a functional for the residual (error estimate)

a_R_T (Form)

the bilinear form for the strong cell residual problem

L_R_T (Form)

the linear form for the strong cell residual problem

a_R_dT (Form)

the bilinear form for the strong facet residual problem

L_R_dT (Form)

the linear form for the strong facet residual problem

eta_T (Form)

a linear form over DG_0 for error indicators

is_linear (bool)

true iff primal problem is linear

static Parameters default_parameters()

Default parameter values:

double estimate_error(const Function& u, const std::vector<std::shared_ptr<const DirichletBC>> bcs)

Estimate the error relative to the goal M of the discrete approximation ‘u’ relative to the variational formulation by evaluating the weak residual at an approximation to the dual solution.

Arguments

u (Function)

the primal approximation

bcs (std::vector<DirichletBC>)

the primal boundary conditions

Returns

double

error estimate

void compute_indicators(MeshFunction<double>& indicators, const Function& u)

Compute error indicators

Arguments

indicators (MeshFunction <double>)

the error indicators (to be computed)

u (Function)

the primal approximation

void residual_representation(Function& R_T, SpecialFacetFunction& R_dT, const Function& u)

Compute strong representation (strong cell and facet residuals) of the weak residual.

Arguments

R_T (Function)

the strong cell residual (to be computed)

R_dT (SpecialFacetFunction)

the strong facet residual (to be computed)

u (Function)

the primal approximation

void compute_cell_residual(Function& R_T, const Function& u)

Compute representation for the strong cell residual from the weak residual

Arguments

R_T (Function)

the strong cell residual (to be computed)

u (Function)

the primal approximation

void compute_facet_residual(SpecialFacetFunction& R_dT, const Function& u, const Function& R_T)

Compute representation for the strong facet residual from the weak residual and the strong cell residual

Arguments

R_dT (SpecialFacetFunction)

the strong facet residual (to be computed)

u (Function)

the primal approximation

R_T (Function)

the strong cell residual

void compute_dual(Function& z, const std::vector<std::shared_ptr<const DirichletBC>> bcs)

Compute dual approximation defined by dual variational problem and dual boundary conditions given by homogenized primal boundary conditions.

Arguments

z (Function)

the dual approximation (to be computed)

bcs (std::vector<DirichletBC>)

the primal boundary conditions

void compute_extrapolation(const Function& z, const std::vector<std::shared_ptr<const DirichletBC>> bcs)

Compute extrapolation with boundary conditions

Arguments

z (Function)

the extrapolated function (to be computed)

bcs (std::vector<DirichletBC>)

the dual boundary conditions