Embedding and a priori wavelet-adaptivity for Dirichlet problems

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 select ing suitable wavelet subspaces. Error estimâtes 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. Received: March 9, 2000. Revised: July 31, 2000.