Discontinuous Galerkin finite element approximation of nondivergence form elliptic equations with Cordès coefficients
Nondivergence form elliptic equations with discontinuous coefficients do not generally possess a weak formulation, thus presenting an obstacle to their numerical solution by classical finite element methods. We propose a new $hp$-version discontinuous Galerkin finite element method for a class of th...
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| Format: | Journal article |
| Language: | English |
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Society for Industrial and Applied Mathematics
2013
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| _version_ | 1826264599974903808 |
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| author | Smears, I Süli, E |
| author_facet | Smears, I Süli, E |
| author_sort | Smears, I |
| collection | OXFORD |
| description | Nondivergence form elliptic equations with discontinuous coefficients do not generally possess a weak formulation, thus presenting an obstacle to their numerical solution by classical finite element methods. We propose a new $hp$-version discontinuous Galerkin finite element method for a class of these problems which satisfy the Cordès condition. It is shown that the method exhibits a convergence rate that is optimal with respect to the mesh size $h$ and suboptimal with respect to the polynomial degree $p$ by only half an order. Numerical experiments demonstrate the accuracy of the method and illustrate the potential of exponential convergence under $hp$-refinement for problems with discontinuous coefficients and nonsmooth solutions. |
| first_indexed | 2024-03-06T20:10:26Z |
| format | Journal article |
| id | oxford-uuid:2a5d4bbb-4d35-43eb-85f9-83be2d3b8324 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:10:26Z |
| publishDate | 2013 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:2a5d4bbb-4d35-43eb-85f9-83be2d3b83242022-03-26T12:24:40ZDiscontinuous Galerkin finite element approximation of nondivergence form elliptic equations with Cordès coefficientsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2a5d4bbb-4d35-43eb-85f9-83be2d3b8324EnglishSymplectic Elements at OxfordSociety for Industrial and Applied Mathematics2013Smears, ISüli, ENondivergence form elliptic equations with discontinuous coefficients do not generally possess a weak formulation, thus presenting an obstacle to their numerical solution by classical finite element methods. We propose a new $hp$-version discontinuous Galerkin finite element method for a class of these problems which satisfy the Cordès condition. It is shown that the method exhibits a convergence rate that is optimal with respect to the mesh size $h$ and suboptimal with respect to the polynomial degree $p$ by only half an order. Numerical experiments demonstrate the accuracy of the method and illustrate the potential of exponential convergence under $hp$-refinement for problems with discontinuous coefficients and nonsmooth solutions. |
| spellingShingle | Smears, I Süli, E Discontinuous Galerkin finite element approximation of nondivergence form elliptic equations with Cordès coefficients |
| title | Discontinuous Galerkin finite element approximation of nondivergence form elliptic equations with Cordès coefficients |
| title_full | Discontinuous Galerkin finite element approximation of nondivergence form elliptic equations with Cordès coefficients |
| title_fullStr | Discontinuous Galerkin finite element approximation of nondivergence form elliptic equations with Cordès coefficients |
| title_full_unstemmed | Discontinuous Galerkin finite element approximation of nondivergence form elliptic equations with Cordès coefficients |
| title_short | Discontinuous Galerkin finite element approximation of nondivergence form elliptic equations with Cordès coefficients |
| title_sort | discontinuous galerkin finite element approximation of nondivergence form elliptic equations with cordes coefficients |
| work_keys_str_mv | AT smearsi discontinuousgalerkinfiniteelementapproximationofnondivergenceformellipticequationswithcordescoefficients AT sulie discontinuousgalerkinfiniteelementapproximationofnondivergenceformellipticequationswithcordescoefficients |