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7.25 Package FL.STRATEGY

This package provides methods for solving problems by adaptive FEM.

Variable: *ETA-OBSERVE*

Observe an estimate of the global error.

Variable: *MENTRIES-OBSERVE*

Observe entries for the size of the matrix.

Variable: *STATIONARY-FE-STRATEGY-OBSERVE*

Standard observe quantities for stationary finite element strategies.

Class: <DUALITY-ERROR-ESTIMATOR>

Estimates the error by testing the difference z-IPz against the residual. Here z is the solution of a dual problem in an enriched finite element space.

Superclasses: <SETUP-ENRICHED-ANSATZ-SPACE> <SOLVE-DUAL-PROBLEM> <LOCAL-TEST-WITH-DUAL> <STANDARD-ERROR-ESTIMATOR>

Class: <FE-APPROXIMATION>

This class describes iterative finite element appoximation strategies.

Superclasses: <STRATEGY>

Direct slots:

Class: <FE-INTERPOLATION>

This class implements adaptive finite element interpolation of the given coefficient function as a variant of finite element approximation.

Superclasses: <FE-APPROXIMATION>

Direct slots:

Class: <LARGEST-ETA-INDICATOR>

Puts the fraction of the cells with the largest error contributions in the refinement table. Note that a fraction of 1.0 yields uniform refinement. Below from-level, global refinement is used. block-p indicates that all children of a parent cell have to be refined at once.

Superclasses: <REFINEMENT-INDICATOR>

Direct slots:

Class: <PROJECTION-ERROR-ESTIMATOR>

Estimates the error by measuring the difference between the solution and a projected solution in a hierarchical mesh by a certain norm given by local-p and global-p.

Superclasses: <DIFFERENCE-WITH-PROJECTION> <GLOBAL-AND-LOCAL-NORM> <STANDARD-ERROR-ESTIMATOR>

Class: <REFINEMENT-INDICATOR>

An indicator is used as first argument in the generic functions indicate which works on a blackboard. Based on the quantities computed by an error estimator, i.e. eta, indicate puts a list of elements to be refined on the blackboard. When ensure-mesh-quality is t, the indicator ensures that the difference of mesh widths of neighboring cells does not become larger than a factor of 4.

Direct slots:

Class: <REGION-INDICATOR>

Marks all cells in a region for refinement.

Superclasses: <REFINEMENT-INDICATOR>

Direct slots:

Class: <ROTHE>

Rothe strategy for time-dependent problems. The idea of the Rothe method for solving U_t +A U =f is to do an ODE time-stepping scheme in an infinite-dimensional function space. Therefore, in every time-step, the solution has to be approximated sufficiently well in the space variable.

Superclasses: <ITERATION>

Direct slots:

Class: <STATIONARY-FE-STRATEGY>

This class describes some iterative finite element solution strategies for continuous, stationary PDE problems.

Superclasses: <FE-APPROXIMATION>

Direct slots:

Class: <STRATEGY>

A strategy is an iteration for solving a problem defined on a blackboard.

Superclasses: <ITERATIVE-SOLVER>

Class: <UNIFORM-REFINEMENT-INDICATOR>

Marks all cells for refinement.

Superclasses: <REFINEMENT-INDICATOR>

Function: ESTIMATE ERROR-ESTIMATOR BLACKBOARD

Yields both local and global estimate.

Function: INDICATE INDICATOR BLACKBOARD

Puts a list of elements to be refined on the blackboard.


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