Volume 54, Number 4, July-August 2020
|Page(s)||1221 - 1257|
|Published online||16 June 2020|
Finite element approximation of elliptic homogenization problems in nondivergence-form
Université de Paris, CNRS, Sorbonne Université, Laboratoire Jacques-Louis Lions UMR 7598, Paris, France
2 University of Oxford, Mathematical Institute, Woodstock Road, Oxford OX2 6GG, UK
Accepted: 18 December 2019
We use uniform W2,p estimates to obtain corrector results for periodic homogenization problems of the form A(x/ε):D2uε = f subject to a homogeneous Dirichlet boundary condition. We propose and rigorously analyze a numerical scheme based on finite element approximations for such nondivergence-form homogenization problems. The second part of the paper focuses on the approximation of the corrector and numerical homogenization for the case of nonuniformly oscillating coefficients. Numerical experiments demonstrate the performance of the scheme.
Mathematics Subject Classification: 35B27 / 35J15 / 65N12 / 65N30
Key words: Homogenization / nondivergence-form elliptic PDE / finite element methods
© The authors. Published by EDP Sciences, SMAI 2020
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