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URN: urn:nbn:de:0030-drops-1381
URL: http://drops.dagstuhl.de/opus/volltexte/2005/138/

Dahlke, Stephan ; Novak, Erich ; Sickel, Winfried

Optimal Approximation of Elliptic Problems II: Wavelet Methods

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Abstract

This talk is concerned with optimal approximations of the solutions of elliptic boundary value problems. After briefly recalling the fundamental concepts of optimality, we shall especially discuss best n-term approximation schemes based on wavelets. We shall mainly be concerned with the Poisson equation in Lipschitz domains. It turns out that wavelet schemes are suboptimal in general, but nevertheless they are superior to the usual uniform approximation methods. Moreover, for specific domains, i.e., for polygonal domains, wavelet methods are in fact optimal. These results are based on regularity estimates of the exact solution in a specific scale of Besov spaces.

BibTeX - Entry

@InProceedings{dahlke_et_al:DSP:2005:138,
  author =	{Stephan Dahlke and Erich Novak and Winfried Sickel},
  title =	{Optimal Approximation of Elliptic Problems II: Wavelet Methods},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  year =	{2005},
  editor =	{Thomas M{\"u}ller-Gronbach and Erich Novak and Knut Petras and Joseph F. Traub},
  number =	{04401},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2005/138},
  annote =	{Keywords: Elliptic operator equations ,  worst case error , best n-term approximation , wavelets , Besov regularity}
}

Keywords: Elliptic operator equations , worst case error , best n-term approximation , wavelets , Besov regularity
Seminar: 04401 - Algorithms and Complexity for Continuous Problems
Issue date: 2005
Date of publication: 19.04.2005


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