Embedding and a priori wavelet-adaptivity for Dirichlet problems

Andreas Rieder

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 6, page 1189-1202
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Rieder, Andreas. "Embedding and a priori wavelet-adaptivity for Dirichlet problems." ESAIM: Mathematical Modelling and Numerical Analysis 34.6 (2010): 1189-1202. <http://eudml.org/doc/197525>.

@article{Rieder2010,
abstract = { 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. },
author = {Rieder, Andreas},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Boundary value problem; fictitious domain; Galerkin scheme; biorthogonal wavelet system; adapted grid.; domain embedding method; Galerkin method; Dirichlet problem; error estimates; adaptivity; compactly supported wavelets; fictitious domain method; numerical experiments},
language = {eng},
month = {3},
number = {6},
pages = {1189-1202},
publisher = {EDP Sciences},
title = {Embedding and a priori wavelet-adaptivity for Dirichlet problems},
url = {http://eudml.org/doc/197525},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Rieder, Andreas
TI - Embedding and a priori wavelet-adaptivity for Dirichlet problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 6
SP - 1189
EP - 1202
AB - 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.
LA - eng
KW - Boundary value problem; fictitious domain; Galerkin scheme; biorthogonal wavelet system; adapted grid.; domain embedding method; Galerkin method; Dirichlet problem; error estimates; adaptivity; compactly supported wavelets; fictitious domain method; numerical experiments
UR - http://eudml.org/doc/197525
ER -

References

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