Finite element approximation of elliptic homogenization problems in nondivergence-form
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...
| Những tác giả chính: | , , |
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| Định dạng: | Journal article |
| Ngôn ngữ: | English |
| Được phát hành: |
EDP Sciences
2020
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| Tóm tắt: | 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. |
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