ErrorControl¶

class dolfin.cpp.fem.ErrorControl(*args)¶

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.

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

compute_cell_residual()¶

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

compute_dual()¶

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 (list of DirichletBC): the primal boundary conditions

compute_extrapolation()¶

Compute extrapolation with boundary conditions

Arguments

z (Function): the extrapolated function (to be computed)
bcs (list of DirichletBC): the dual boundary conditions

compute_facet_residual()¶

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

compute_indicators()¶

Compute error indicators

Arguments

indicators (MeshFunction): the error indicators (to be computed)
u (Function): the primal approximation

static default_parameters(*args)¶: Default parameter values:

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.

Arguments

u (Function): the primal approximation
bcs (list of DirichletBC): the primal boundary conditions

Returns

float: error estimate

residual_representation()¶

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

thisown¶: The membership flag