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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:

- 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. 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:

- FRACTION: Self-explanatory.
- PIVOT-FACTOR: Self-explanatory.
- FROM-LEVEL: Self-explanatory.
- BLOCK-P: 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 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:

- ENSURE-MESH-QUALITY: Self-explanatory.

- Class:
**<REGION-INDICATOR>** -
Marks all cells in a region for refinement.

Superclasses: <REFINEMENT-INDICATOR>

Direct slots:

- IN-REGION: Self-explanatory.

- 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:

- MODEL-TIME: Current time in the time-stepping scheme.
- TIME-STEP: Self-explanatory.
- SCHEME: Time-stepping scheme,
e.g.
`:implicit-euler`

or`:crank-nicolson`

. - 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 elements to be refined on the blackboard.

Next: Package FL.GRAPHIC, Previous: Package FL.GEOMG, Up: Reference manual [Contents][Index]