Adaptive Local (AL) Basis for Elliptic Problems with $L^{\infty }$-Coefficients

Abstract

We define a generalized finite element method for the discretization of elliptic partial differential equations in heterogeneous media. An adaptive local finite element basis (AL basis) on a coarse mesh which does not resolve the matrix of the media is constructed by solving finite-dimensional localized problems. The method requires $O(log(1/H{)}^{d+1})$ basis functions per mesh point. We prove that the optimal finite element convergence rates are preserved.

arXiv comment25 pages, 1 figure

Cited by in corpus (1)

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