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Optimal Approximation of Elliptic Problems II: Wavelet Methods

Authors Stephan Dahlke, Erich Novak, Winfried Sickel

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Keywords
  • Elliptic operator equations
  • worst case error
  • best n-term approximation
  • wavelets
  • Besov regularity

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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.

Cite As Get BibTex

Stephan Dahlke, Erich Novak, and Winfried Sickel. Optimal Approximation of Elliptic Problems II: Wavelet Methods. In Algorithms and Complexity for Continuous Problems. Dagstuhl Seminar Proceedings, Volume 4401, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005) https://doi.org/10.4230/DagSemProc.04401.13

Author Details

Stephan Dahlke
Erich Novak
Winfried Sickel
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