Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity
We consider the a posteriori error analysis and hp-adaptation strategies for hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes with anisotropically enriched e...
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| Online Access: | https://eprints.nottingham.ac.uk/670/ |
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| author | Georgoulis, Emmanuil H. Hall, Edward Houston, Paul |
| author_facet | Georgoulis, Emmanuil H. Hall, Edward Houston, Paul |
| author_sort | Georgoulis, Emmanuil H. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We consider the a posteriori error analysis and hp-adaptation strategies for hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes with anisotropically enriched elemental polynomial degrees. In particular, we exploit duality based hp-error estimates for linear target functionals of the solution and design and implement the corresponding adaptive algorithms to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local isotropic and anisotropic mesh refinement and isotropic and anisotropic polynomial degree enrichment. The superiority of the proposed algorithm in comparison with standard hp-isotropic mesh refinement algorithms and an h-anisotropic/p-isotropic adaptive procedure is illustrated by a series of numerical experiments. |
| first_indexed | 2025-11-14T18:12:58Z |
| format | Article |
| id | nottingham-670 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:12:58Z |
| recordtype | eprints |
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| spelling | nottingham-6702020-05-04T20:34:35Z https://eprints.nottingham.ac.uk/670/ Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity Georgoulis, Emmanuil H. Hall, Edward Houston, Paul We consider the a posteriori error analysis and hp-adaptation strategies for hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes with anisotropically enriched elemental polynomial degrees. In particular, we exploit duality based hp-error estimates for linear target functionals of the solution and design and implement the corresponding adaptive algorithms to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local isotropic and anisotropic mesh refinement and isotropic and anisotropic polynomial degree enrichment. The superiority of the proposed algorithm in comparison with standard hp-isotropic mesh refinement algorithms and an h-anisotropic/p-isotropic adaptive procedure is illustrated by a series of numerical experiments. Article NonPeerReviewed Georgoulis, Emmanuil H., Hall, Edward and Houston, Paul Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity. Applied Numerical Mathematics . (Submitted) |
| spellingShingle | Georgoulis, Emmanuil H. Hall, Edward Houston, Paul Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity |
| title | Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity |
| title_full | Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity |
| title_fullStr | Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity |
| title_full_unstemmed | Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity |
| title_short | Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity |
| title_sort | discontinuous galerkin methods on hp-anisotropic meshes ii: a posteriori error analysis and adaptivity |
| url | https://eprints.nottingham.ac.uk/670/ |