Abstract
This paper is concerned with some theoretical foundations for adaptive numerical methods for elliptic boundary value problems. The approximation order that can be achieved by such an adaptive method is determined by certain Besov regularity of the weak solution. We study Besov regularity for second order elliptic problems in bounded domains in ℝd. The investigations are based on intermediate Schauder estimates and on some potential theoretic framework. Moreover, we use characterizations of Besov spaces by wavelet expansions.
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This work has been supported by the Deutsche Forschungsgemeinschaft (Da 360/1-1)
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Dahlke, S. Besov regularity for second order elliptic boundary value problems with variable coefficients. Manuscripta Math 95, 59–77 (1998). https://doi.org/10.1007/BF02678015
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DOI: https://doi.org/10.1007/BF02678015
Key Words
- elliptic boundary value problems
- adaptive methods
- nonlinear approximation
- Besov spaces
- wavelets
- Schauder estimates
- potential theory