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: *FE-APPROXIMATION-OBSERVE*

Standard observe quantities for fe approximation.

Variable: *MENTRIES-OBSERVE*

Observe entries for the size of the matrix.

Variable: *ROTHE-OBSERVE*

Standard observe quantities for Rothe.

Variable: *STATIONARY-FE-STRATEGY-OBSERVE*

Standard observe quantities for stationary finite element strategies.

Class: <CELL-RULE-INDICATOR>

Calls cell-rule on a cell for determinining its refinement rule.

Superclasses: <REFINEMENT-INDICATOR>

Direct slots:

• CELL-RULE: Self-explanatory.

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:

• OBSERVE: Providing initform for <iteration> slot.
• PLOT-MESH: Plot the mesh at the beginning and after changes. Can be a function in which case it is called on the mesh to do the plotting.
• FE-CLASS: The class of finite element. If it is not set, it is automatically chosen.
• ESTIMATOR: The error estimator, which computes information on the error distribution in a hash-table in the :ETA-field on the blackboard, as well as a global estimate in :GLOBAL-ETA which can be used to terminate the iteration.
• INDICATOR: The error indicator which marks cells for local refinement. Usually, this procedure will be based on the error distribution approximated in the :ETA-field on the blackboard.

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:

• COEFFICIENT: A coefficient determining the function to be interpolated.

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.

Superclasses: <REFINEMENT-INDICATOR>

Direct slots:

• FRACTION: Self-explanatory.
• PIVOT-FACTOR: Self-explanatory.

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 error indicator can appear as first argument in the indicate which works on a blackboard. Often, it will use quantities computed by an error estimator before.

Direct slots:

• TOP-LEVEL: If top-level is set, no refinement beyond top-level is indicated.
• FROM-LEVEL: Below from-level, global refinement is used. If from-level=NIL, regular global refinement is indicated, if no other indication is available.
• BLOCK-P: If block-p is T, all children of a parent cell are indicated for refinement together.
• ENSURE-MESH-QUALITY-P: If ensure-mesh-quality-p is T, the indicator ensures that the difference of mesh widths of neighboring cells does not become larger than a factor of 4.

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: <ITERATIVE-SOLVER>

Direct slots:

• MODEL-TIME: Current time in the time-stepping scheme.
• TIME-STEP: Self-explanatory.
• OLD-TIME-STEP: For use in BDF formula
• MINIMAL-TIME-STEP: Self-explanatory.
• MAXIMAL-TIME-STEP: Self-explanatory.
• FORCED-TIMES: Self-explanatory.
• SCHEME: Time-stepping scheme, e.g. :implicit-euler or :bdf2.
• STATIONARY-SUCCESS-IF: Self-explanatory.
• STATIONARY-FAILURE-IF: Self-explanatory.
• PLOT: Self-explanatory.
• OBSERVE: Providing initform for <iteration> slot.

Class: <STATIONARY-FE-STRATEGY>

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

Superclasses: <FE-APPROXIMATION>

Direct slots:

• OBSERVE: Self-explanatory.
• SOLVER: The solver for solving the discretized systems.

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 cells to be refined on the blackboard.

Function: POINT-OBSERVE POSITION &KEY (COMPONENT 0) (INDEX 0)

Generates an observer triple which observes the value of component component of solution number index at the position position.