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The AL Basis for the solution of elliptic problems in heterogeneous media


Grasedyk, L; Greff, I; Sauter, S (2012). The AL Basis for the solution of elliptic problems in heterogeneous media. Multiscale Modeling & Simulation, 10(1):245-258.

Abstract

In this paper, we will show that, for elliptic problems in heterogeneous media, there exists a local ( generalized) finite element basis (AL basis) consisting of O((log 1/H)(d+1) basis functions per nodal point such that the convergence rates of the classical finite element method for Poisson- type problems are preserved. Here H denotes the mesh width of the finite element mesh and d is the spatial dimension. We provide several numerical examples beyond our theory, where even O( 1) basis functions per nodal point are sufficient to preserve the convergence rates.

Abstract

In this paper, we will show that, for elliptic problems in heterogeneous media, there exists a local ( generalized) finite element basis (AL basis) consisting of O((log 1/H)(d+1) basis functions per nodal point such that the convergence rates of the classical finite element method for Poisson- type problems are preserved. Here H denotes the mesh width of the finite element mesh and d is the spatial dimension. We provide several numerical examples beyond our theory, where even O( 1) basis functions per nodal point are sufficient to preserve the convergence rates.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2012
Deposited On:25 Jan 2013 15:28
Last Modified:17 Feb 2018 00:44
Publisher:Society for Industrial and Applied Mathematics
ISSN:1540-3459
OA Status:Green
Publisher DOI:https://doi.org/10.1137/11082138X

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