Embedding and a priori wavelet-adaptivity for Dirichlet problems
Institut für Wissenschaftliches Rechnen
und Mathematische Modellbildung (IWRMM), Universität Karlsruhe, 76128 Karlsruhe, Germany.
Revised: 31 July 2000
The accuracy of the domain embedding method from [A. Rieder, Modél. Math. Anal. Numér. 32 (1998) 405-431] for the solution of Dirichlet problems suffers under a coarse boundary approximation. To overcome this drawback the method is furnished with an 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 the literature our approach combines a high generality with an easy-to-implement algorithm.
Mathematics Subject Classification: 65N30 / 65N50
Key words: Boundary value problem / fictitious domain / Galerkin scheme / biorthogonal wavelet system / adapted grid.
© EDP Sciences, SMAI, 2000