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)

(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

@param a_star (Form)
the bilinear form for the dual problem
@param L_star (Form)
the linear form for the dual problem
@param residual (Form)
a functional for the residual (error estimate)
@param a_R_T (Form)
the bilinear form for the strong cell residual problem
@param L_R_T (Form)
the linear form for the strong cell residual problem
@param a_R_dT (Form)
the bilinear form for the strong facet residual problem
@param L_R_dT (Form)
the linear form for the strong facet residual problem
@param eta_T (Form)
a linear form over DG_0 for error indicators
@param 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.

@param u (Function)
the primal approximation
@param bcs (std::vector<DirichletBC>)
the primal boundary conditions
@return double
error estimate
void compute_indicators(MeshFunction<double> &indicators, const Function &u)

Compute error indicators

@param indicators (MeshFunction<double>)
the error indicators (to be computed)
@param 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.

@param R_T (Function)
the strong cell residual (to be computed)
@param R_dT (SpecialFacetFunction)
the strong facet residual (to be computed)
@param 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

@param R_T (Function)
the strong cell residual (to be computed)
@param 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

@param R_dT (SpecialFacetFunction)
the strong facet residual (to be computed)
@param u (Function)
the primal approximation
@param 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.

@param z (Function)
the dual approximation (to be computed)
@param 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

@param z (Function)
the extrapolated function (to be computed)
@param bcs (std::vector<DirichletBC>)
the dual boundary conditions