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...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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EDP Sciences
2020
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| _version_ | 1797076459418812416 |
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| author | Capdeboscq, Y Sprekeler, T Süli, E |
| author_facet | Capdeboscq, Y Sprekeler, T Süli, E |
| author_sort | Capdeboscq, Y |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T00:04:05Z |
| format | Journal article |
| id | oxford-uuid:76f3da12-91d8-4eac-afa5-df42d04dff1d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:04:05Z |
| publishDate | 2020 |
| publisher | EDP Sciences |
| record_format | dspace |
| spelling | oxford-uuid:76f3da12-91d8-4eac-afa5-df42d04dff1d2022-03-26T20:19:54ZFinite element approximation of elliptic homogenization problems in nondivergence-formJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:76f3da12-91d8-4eac-afa5-df42d04dff1dEnglishSymplectic Elements at OxfordEDP Sciences2020Capdeboscq, YSprekeler, TSüli, EWe 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. |
| spellingShingle | Capdeboscq, Y Sprekeler, T Süli, E Finite element approximation of elliptic homogenization problems in nondivergence-form |
| title | Finite element approximation of elliptic homogenization problems in nondivergence-form |
| title_full | Finite element approximation of elliptic homogenization problems in nondivergence-form |
| title_fullStr | Finite element approximation of elliptic homogenization problems in nondivergence-form |
| title_full_unstemmed | Finite element approximation of elliptic homogenization problems in nondivergence-form |
| title_short | Finite element approximation of elliptic homogenization problems in nondivergence-form |
| title_sort | finite element approximation of elliptic homogenization problems in nondivergence form |
| work_keys_str_mv | AT capdeboscqy finiteelementapproximationofelliptichomogenizationproblemsinnondivergenceform AT sprekelert finiteelementapproximationofelliptichomogenizationproblemsinnondivergenceform AT sulie finiteelementapproximationofelliptichomogenizationproblemsinnondivergenceform |