Discontinuous Galerkin methods for problems with Dirac delta source
In this article we study discontinuous Galerkin finite element discretizations of linear second-order elliptic partial differential equations with Dirac delta right-hand side. In particular, assuming that the underlying computational mesh is quasi-uniform, we derive an a priori bound on the error me...
| Main Authors: | , |
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| Format: | Article |
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EDP
2011
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| Online Access: | https://eprints.nottingham.ac.uk/1499/ |
| _version_ | 1848790618037288960 |
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| author | Houston, Paul Wihler, Thomas P. |
| author_facet | Houston, Paul Wihler, Thomas P. |
| author_sort | Houston, Paul |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In this article we study discontinuous Galerkin finite element discretizations of linear second-order elliptic partial differential equations with Dirac delta right-hand side. In particular, assuming that the underlying computational mesh is quasi-uniform, we derive an a priori bound on the error measured in terms of the L^2-norm. Additionally, we develop residual-based a posteriori error estimators that can be used within an adaptive mesh refinement framework. Numerical examples for the symmetric interior penalty scheme are presented which confirm the theoretical results. |
| first_indexed | 2025-11-14T18:15:28Z |
| format | Article |
| id | nottingham-1499 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:15:28Z |
| publishDate | 2011 |
| publisher | EDP |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-14992020-05-04T20:23:56Z https://eprints.nottingham.ac.uk/1499/ Discontinuous Galerkin methods for problems with Dirac delta source Houston, Paul Wihler, Thomas P. In this article we study discontinuous Galerkin finite element discretizations of linear second-order elliptic partial differential equations with Dirac delta right-hand side. In particular, assuming that the underlying computational mesh is quasi-uniform, we derive an a priori bound on the error measured in terms of the L^2-norm. Additionally, we develop residual-based a posteriori error estimators that can be used within an adaptive mesh refinement framework. Numerical examples for the symmetric interior penalty scheme are presented which confirm the theoretical results. EDP 2011 Article NonPeerReviewed Houston, Paul and Wihler, Thomas P. (2011) Discontinuous Galerkin methods for problems with Dirac delta source. ESAIM: Mathematical Modelling and Numerical Analysis . ISSN 0764-583X (Submitted) http://www.esaim-m2an.org/action/displayJournal?jid=MZA |
| spellingShingle | Houston, Paul Wihler, Thomas P. Discontinuous Galerkin methods for problems with Dirac delta source |
| title | Discontinuous Galerkin methods for problems with Dirac delta source |
| title_full | Discontinuous Galerkin methods for problems with Dirac delta source |
| title_fullStr | Discontinuous Galerkin methods for problems with Dirac delta source |
| title_full_unstemmed | Discontinuous Galerkin methods for problems with Dirac delta source |
| title_short | Discontinuous Galerkin methods for problems with Dirac delta source |
| title_sort | discontinuous galerkin methods for problems with dirac delta source |
| url | https://eprints.nottingham.ac.uk/1499/ https://eprints.nottingham.ac.uk/1499/ |