Second-order elliptic PDE with discontinuous boundary data
We shall consider the weak formulation of a linear elliptic model problem with discontinuous Dirichlet boundary conditions. Since such problems are typically not well-defined in the standard H^1-H^1 setting, we will introduce a suitable saddle point formulation in terms of weighted Sobolev spaces. F...
| Main Authors: | , |
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| Format: | Article |
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Oxford University Press
2009
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| Online Access: | https://eprints.nottingham.ac.uk/1215/ |
| _version_ | 1848790562171256832 |
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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 | We shall consider the weak formulation of a linear elliptic model problem with discontinuous Dirichlet boundary conditions. Since such problems are typically not well-defined in the standard H^1-H^1 setting, we will introduce a suitable saddle point formulation in terms of weighted Sobolev spaces. Furthermore, we will discuss the numerical solution of such problems. Specifically, we employ an hp-discontinuous Galerkin method and derive an L^2-norm a posteriori error estimate. Numerical experiments demonstrate the effectiveness of the proposed error indicator in both the h- and hp-version setting. Indeed, in the latter case exponential convergence of the error is attained as the mesh is adaptively refined. |
| first_indexed | 2025-11-14T18:14:35Z |
| format | Article |
| id | nottingham-1215 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:14:35Z |
| publishDate | 2009 |
| publisher | Oxford University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-12152020-05-04T20:26:06Z https://eprints.nottingham.ac.uk/1215/ Second-order elliptic PDE with discontinuous boundary data Houston, Paul Wihler, Thomas P. We shall consider the weak formulation of a linear elliptic model problem with discontinuous Dirichlet boundary conditions. Since such problems are typically not well-defined in the standard H^1-H^1 setting, we will introduce a suitable saddle point formulation in terms of weighted Sobolev spaces. Furthermore, we will discuss the numerical solution of such problems. Specifically, we employ an hp-discontinuous Galerkin method and derive an L^2-norm a posteriori error estimate. Numerical experiments demonstrate the effectiveness of the proposed error indicator in both the h- and hp-version setting. Indeed, in the latter case exponential convergence of the error is attained as the mesh is adaptively refined. Oxford University Press 2009-12 Article NonPeerReviewed Houston, Paul and Wihler, Thomas P. (2009) Second-order elliptic PDE with discontinuous boundary data. IMA Journal of Numerical Analysis . ISSN 0272-4979 (Submitted) http://imajna.oxfordjournals.org/ |
| spellingShingle | Houston, Paul Wihler, Thomas P. Second-order elliptic PDE with discontinuous boundary data |
| title | Second-order elliptic PDE with discontinuous boundary data |
| title_full | Second-order elliptic PDE with discontinuous boundary data |
| title_fullStr | Second-order elliptic PDE with discontinuous boundary data |
| title_full_unstemmed | Second-order elliptic PDE with discontinuous boundary data |
| title_short | Second-order elliptic PDE with discontinuous boundary data |
| title_sort | second-order elliptic pde with discontinuous boundary data |
| url | https://eprints.nottingham.ac.uk/1215/ https://eprints.nottingham.ac.uk/1215/ |