Projection techniques embedded in the PCGM for handling hanging nodes and boundary restrictions

Authors:
A. Meyer
Affiliations:
Faculty of Mathematics, Technical University of Chemnitz, Germany
Venue:
Engineering computational technology
Year:
2002

Citing 4
Cited 3

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Abstract

We consider an adaptive finite element method using so called 'hanging nodes' from subdividing an edge of the actual finite element mesh and subdividing only one of the adjacent triangles (or quadrilaterals) at this edge. The solution method of the resulting linear system requires a solution belonging to a special subspace that generates a conformal finite element function. We discuss the use of a special projection operator within the preconditioned conjugate gradient method and a favorable implementation of this projection in combination with the hierarchical finite element basis for linear and quadratic elements. Analogously, projections onto boundary restrictions are incorporated. The final adaptive run is demonstrated by means of a Signorini contact problem.