Error Estimates for Finite Element Discretizations of Elliptic Problems with Oscillatory Coefficients
Please always quote using this URN:urn:nbn:de:0296-matheon-7394
- In this paper we will consider elliptic boundary value problems with oscillatory diffusion coefficient, say A. We will derive regularity estimates in Sobolev norms which are weighted by certain derivatives of A. The constants in the regularity estimates then turn out to be independent of the variations in A. These regularity results will be employed for the derivation of error estimates for hp-finite element discretizations which are explicit with respect to the local variations of the diffusion coefficient.
Author: | Daniel Peterseim, Stefan Sauter |
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URN: | urn:nbn:de:0296-matheon-7394 |
Referee: | Carsten Carstensen |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2011/12/01 |
Release Date: | 2010/12/15 |
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Institute: | Research Center Matheon |
Humboldt-Universität zu Berlin | |
MSC-Classification: | 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B65 Smoothness and regularity of solutions |
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J57 Boundary value problems for second-order elliptic systems | |
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods | |
Preprint Number: | 756 |