Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes
In this paper we consider the a posteriori and a priori error analysis of discontinuous Galerkin interior penalty methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes. In particular, we discuss the question of er...
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| Format: | Article |
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2006
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| Online Access: | https://eprints.nottingham.ac.uk/424/ |
| _version_ | 1848790410541924352 |
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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 | In this paper we consider the a posteriori and a priori error analysis of discontinuous Galerkin interior penalty methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes. In particular, we discuss the question of error estimation for linear target functionals, such as the outflow flux and the local average of the solution. Based on our a posteriori error bound we design and implement the corresponding adaptive algorithm 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. The theoretical results are illustrated by a series of numerical experiments. |
| first_indexed | 2025-11-14T18:12:10Z |
| format | Article |
| id | nottingham-424 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:12:10Z |
| publishDate | 2006 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-4242020-05-04T20:29:52Z https://eprints.nottingham.ac.uk/424/ Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes Georgoulis, Emmanuil H. Hall, Edward Houston, Paul In this paper we consider the a posteriori and a priori error analysis of discontinuous Galerkin interior penalty methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes. In particular, we discuss the question of error estimation for linear target functionals, such as the outflow flux and the local average of the solution. Based on our a posteriori error bound we design and implement the corresponding adaptive algorithm 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. The theoretical results are illustrated by a series of numerical experiments. 2006 Article NonPeerReviewed Georgoulis, Emmanuil H., Hall, Edward and Houston, Paul (2006) Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes. Anisotropic mesh adaptation discontinuous Galerkin methods PDEs with nonnegative characteristic form |
| spellingShingle | Anisotropic mesh adaptation discontinuous Galerkin methods PDEs with nonnegative characteristic form Georgoulis, Emmanuil H. Hall, Edward Houston, Paul Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes |
| title | Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes |
| title_full | Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes |
| title_fullStr | Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes |
| title_full_unstemmed | Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes |
| title_short | Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes |
| title_sort | discontinuous galerkin methods for advection-diffusion-reaction problems on anisotropically refined meshes |
| topic | Anisotropic mesh adaptation discontinuous Galerkin methods PDEs with nonnegative characteristic form |
| url | https://eprints.nottingham.ac.uk/424/ |