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Finite element approximation of elliptic homogenization problems in nondivergence-form

Abstract:
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.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1051/m2an/2019093

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Institution:
University of Oxford
Department:
Mathematical Institute
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
EDP Sciences Publisher's website
Journal:
ESAIM: Mathematical Modelling and Numerical Analysis Journal website
Volume:
54
Issue:
4
Pages:
1221-1257
Publication date:
2020-06-16
Acceptance date:
2019-12-18
DOI:
EISSN:
1290-3841
ISSN:
0764-583X
Source identifiers:
1010765
Language:
English
Keywords:
Pubs id:
pubs:1010765
UUID:
uuid:76f3da12-91d8-4eac-afa5-df42d04dff1d
Local pid:
pubs:1010765
Deposit date:
2019-10-12

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