We use uniform W$$ estimates to obtain corrector results for periodic homogenization problems of the form $$ 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.
Keywords: Homogenization, nondivergence-form elliptic PDE, finite element methods
@article{M2AN_2020__54_4_1221_0,
author = {Capdeboscq, Yves and Sprekeler, Timo and S\"uli, Endre},
title = {Finite element approximation of elliptic homogenization problems in nondivergence-form},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1221--1257},
year = {2020},
publisher = {EDP Sciences},
volume = {54},
number = {4},
doi = {10.1051/m2an/2019093},
mrnumber = {4111657},
zbl = {1445.35028},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2019093/}
}
TY - JOUR AU - Capdeboscq, Yves AU - Sprekeler, Timo AU - Süli, Endre TI - Finite element approximation of elliptic homogenization problems in nondivergence-form JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2020 SP - 1221 EP - 1257 VL - 54 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2019093/ DO - 10.1051/m2an/2019093 LA - en ID - M2AN_2020__54_4_1221_0 ER -
%0 Journal Article %A Capdeboscq, Yves %A Sprekeler, Timo %A Süli, Endre %T Finite element approximation of elliptic homogenization problems in nondivergence-form %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2020 %P 1221-1257 %V 54 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2019093/ %R 10.1051/m2an/2019093 %G en %F M2AN_2020__54_4_1221_0
Capdeboscq, Yves; Sprekeler, Timo; Süli, Endre. Finite element approximation of elliptic homogenization problems in nondivergence-form. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 4, pp. 1221-1257. doi: 10.1051/m2an/2019093
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