Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems.
We develop the convergence analysis of discontinuous Galerkin finite element approximations to symmetric second-order quasi-linear elliptic and hyperbolic systems of partial differential equations in divergence form in a bounded spatial domain in ℝd, subject to mixed Dirichlet-Neumann boundary condi...
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| Format: | Journal article |
| Language: | English |
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2007
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| _version_ | 1797092564892909568 |
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| author | Ortner, C Süli, E |
| author_facet | Ortner, C Süli, E |
| author_sort | Ortner, C |
| collection | OXFORD |
| description | We develop the convergence analysis of discontinuous Galerkin finite element approximations to symmetric second-order quasi-linear elliptic and hyperbolic systems of partial differential equations in divergence form in a bounded spatial domain in ℝd, subject to mixed Dirichlet-Neumann boundary conditions. Optimal-order asymptotic bounds are derived on the discretization error in each case without requiring the global Lipschitz continuity or uniform monotonicity of the stress tensor. Instead, only local smoothness and a Gårding inequality are used in the analysis. © 2007 Society for Industrial and Applied Mathematics. |
| first_indexed | 2024-03-07T03:47:46Z |
| format | Journal article |
| id | oxford-uuid:c01c0731-8c3d-43b9-a6d3-5ba1a00a2178 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:47:46Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:c01c0731-8c3d-43b9-a6d3-5ba1a00a21782022-03-27T05:52:14ZDiscontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c01c0731-8c3d-43b9-a6d3-5ba1a00a2178EnglishSymplectic Elements at Oxford2007Ortner, CSüli, EWe develop the convergence analysis of discontinuous Galerkin finite element approximations to symmetric second-order quasi-linear elliptic and hyperbolic systems of partial differential equations in divergence form in a bounded spatial domain in ℝd, subject to mixed Dirichlet-Neumann boundary conditions. Optimal-order asymptotic bounds are derived on the discretization error in each case without requiring the global Lipschitz continuity or uniform monotonicity of the stress tensor. Instead, only local smoothness and a Gårding inequality are used in the analysis. © 2007 Society for Industrial and Applied Mathematics. |
| spellingShingle | Ortner, C Süli, E Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems. |
| title | Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems. |
| title_full | Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems. |
| title_fullStr | Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems. |
| title_full_unstemmed | Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems. |
| title_short | Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems. |
| title_sort | discontinuous galerkin finite element approximation of nonlinear second order elliptic and hyperbolic systems |
| work_keys_str_mv | AT ortnerc discontinuousgalerkinfiniteelementapproximationofnonlinearsecondorderellipticandhyperbolicsystems AT sulie discontinuousgalerkinfiniteelementapproximationofnonlinearsecondorderellipticandhyperbolicsystems |