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DOI: 10.4230/DagSemProc.04401.13
URN: urn:nbn:de:0030-drops-1381
URL: https://drops.dagstuhl.de/opus/volltexte/2005/138/
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Dahlke, Stephan ; Novak, Erich ; Sickel, Winfried

Optimal Approximation of Elliptic Problems II: Wavelet Methods

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04401.DahlkeStephan.ExtAbstract.138.pdf (0.1 MB)


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:DagSemProc.04401.13,
  author =	{Dahlke, Stephan and Novak, Erich and Sickel, Winfried},
  title =	{{Optimal Approximation of Elliptic Problems II: Wavelet Methods}},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4401},
  editor =	{Thomas M\"{u}ller-Gronbach and Erich Novak and Knut Petras and Joseph F. Traub},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2005/138},
  URN =		{urn:nbn:de:0030-drops-1381},
  doi =		{10.4230/DagSemProc.04401.13},
  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
Collection: 04401 - Algorithms and Complexity for Continuous Problems
Issue Date: 2005
Date of publication: 19.04.2005


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