ErrorControl

class dolfin.cpp.fem.ErrorControl

Bases: dolfin.cpp.fem.HierarchicalErrorControl, dolfin.cpp.common.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.

Friends: adapt.

Create error control object

Parameters:
  • Form > a_star (std::shared_ptr<) – (Form ) the bilinear form for the dual problem
  • Form > L_star (std::shared_ptr<) – (Form ) the linear form for the dual problem
  • Form > residual (std::shared_ptr<) – (Form ) a functional for the residual (error estimate)
  • Form > a_R_T (std::shared_ptr<) – (Form ) the bilinear form for the strong cell residual problem
  • Form > L_R_T (std::shared_ptr<) – (Form ) the linear form for the strong cell residual problem
  • Form > a_R_dT (std::shared_ptr<) – (Form ) the bilinear form for the strong facet residual problem
  • Form > L_R_dT (std::shared_ptr<) – (Form ) the linear form for the strong facet residual problem
  • Form > eta_T (std::shared_ptr<) – (Form ) a linear form over DG_0 for error indicators
  • is_linear (bool) – (bool) true iff primal problem is linear
compute_cell_residual()

Compute representation for the strong cell residual from the weak residual

Parameters:
  • & R_T (Function) – (Function ) the strong cell residual (to be computed)
  • Function & u (const) – (Function ) the primal approximation
Return type:

void
compute_dual()

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

Parameters:
  • & z (Function) – (Function ) the dual approximation (to be computed)
  • std::vector< std::shared_ptr< const DirichletBC > > bcs (const) – (std::vector<DirichletBC>) the primal boundary conditions
Return type:

void
compute_extrapolation()

Compute extrapolation with boundary conditions

Parameters:
  • Function & z (const) – (Function ) the extrapolated function (to be computed)
  • std::vector< std::shared_ptr< const DirichletBC > > bcs (const) – (std::vector<DirichletBC >) the dual boundary conditions
Return type:

void
compute_facet_residual()

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

Parameters:
  • & R_dT (SpecialFacetFunction) – (SpecialFacetFunction ) the strong facet residual (to be computed)
  • Function & u (const) – (Function ) the primal approximation
  • Function & R_T (const) – (Function ) the strong cell residual
Return type:

void
compute_indicators()

Compute error indicators

Parameters:
  • double > & indicators (MeshFunction<) – (MeshFunction<double>) the error indicators (to be computed)
  • Function & u (const) – (Function ) the primal approximation
Return type:

void
static default_parameters()
estimate_error()

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.

Parameters:
  • Function & u (const) – (Function ) the primal approximation
  • std::vector< std::shared_ptr< const DirichletBC > > bcs (const) – (std::vector<DirichletBC >) the primal boundary conditions
Return type:

double
Returns:

double error estimate
residual_representation()

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

Parameters:
  • & R_T (Function) – (Function ) the strong cell residual (to be computed)
  • & R_dT (SpecialFacetFunction) – (SpecialFacetFunction ) the strong facet residual (to be computed)
  • Function & u (const) – (Function ) the primal approximation
Return type:

void
thisown

The membership flag