ErrorControl

class dolfin.cpp.fem.ErrorControl(a_star, L_star, residual, a_R_T, L_R_T, a_R_dT, L_R_dT, eta_T, is_linear)

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()

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