Optimal Approximation of Elliptic Problems II: Wavelet Methods

Authors Stephan Dahlke, Erich Novak, Winfried Sickel

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Stephan Dahlke
Erich Novak
Winfried Sickel

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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)


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


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