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Embedding and a priori wavelet-adaptivityforDirichlet problems

Published online by Cambridge University Press:  15 April 2002

Andreas Rieder
Andreas Rieder*
Affiliation:
Institut für Wissenschaftliches Rechnen und Mathematische Modellbildung (IWRMM), Universität Karlsruhe, 76128 Karlsruhe, Germany. email: andreas.rieder@math.uni-karlsruhe.de
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Abstract

The accuracy of the domain embedding method from [A. Rieder, Modél. Math. Anal. Numér.32 (1998) 405-431] for the solution of Dirichlet problemssuffers under a coarse boundary approximation. To overcome this drawback the methodis furnished withan a priori (static) strategy for an adaptive approximation space refinement near the boundary. This is done by selecting suitable wavelet subspaces. Error estimates and numerical experiments validate the proposed adaptive scheme.In contrast to similar, but rather theoretical, concepts already described in theliterature our approach combines a high generality with an easy-to-implement algorithm.

Keywords

Boundary value problemfictitious domainGalerkin schemebiorthogonal wavelet systemadapted grid.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 6 , November 2000 , pp. 1189 - 1202
Copyright
© EDP Sciences, SMAI, 2000

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