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

Monika Weymuth

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

Numerical Analysis 2017-03-21 v1

Authors: Monika Weymuth

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.

Keywords

finite element method finite element methods mixed finite element methods

Cite

@article{arxiv.1703.06325,
  title  = {Adaptive Local (AL) Basis for Elliptic Problems with $L^\infty$-Coefficients},
  author = {Monika Weymuth},
  journal= {arXiv preprint arXiv:1703.06325},
  year   = {2017}
}

Comments

25 pages, 1 figure

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