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Localization of Elliptic Multiscale Problems

Please always quote using this URN:urn:nbn:de:0296-matheon-9046
  • This note constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying diffusion tensor. The basis functions are solutions of local problems on vertex patches. The error of the corresponding generalized finite element method decays exponentially w.r.t. the number of element layers in the patches. Hence, on a uniform mesh of size H, patches of diameter log(1/H) are sufficient to preserve the convergence rates of the classical P1-FEM for the Poisson problem. The analysis does not rely on regularity of the solution or scale separation in the coefficient. The result justifies the use of the class of variational multiscale methods, introduced in [Comput. Methods Appl. Mech. Engrg., 196:2313--2324, 2007].

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Metadaten
Author:Axel Malqvist, Daniel Peterseim
URN:urn:nbn:de:0296-matheon-9046
Referee:Ralf Kornhuber
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/10/11
Release Date:2011/10/11
Tag:
Institute:Research Center Matheon
Humboldt-Universität zu Berlin
Project:C Energy and Materials (Production)
MSC-Classification:65-XX NUMERICAL ANALYSIS
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N12 Stability and convergence of numerical methods
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems
Preprint Number:820
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