Adaptive Local (AL) Basis for Elliptic Problems with L^∞-Coefficients

2017/03/18 by Monika Weymuth, Weymuth, Monika
Computer Science · Engineering · #35R05 #65N12 #65N15 #65N30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1703.06325

openalex publication_date 2017/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

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