Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs
In this article we develop the a priori error analysis of so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical approximation of strongly monotone second-order quasilinear partial differential equations. In this setting, the fully nonlinear problem is first ap...
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| Format: | Article |
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Wiley-VCH
2011
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| Online Access: | https://eprints.nottingham.ac.uk/1481/ |
| _version_ | 1848790614910435328 |
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| author | Congreve, Scott Houston, Paul Wihler, Thomas P. |
| author_facet | Congreve, Scott Houston, Paul Wihler, Thomas P. |
| author_sort | Congreve, Scott |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In this article we develop the a priori error analysis of so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical approximation of strongly monotone second-order quasilinear partial differential equations. In this setting, the fully nonlinear problem is first approximated on a coarse finite element space V(H,P). The resulting `coarse' numerical solution is then exploited to provide the necessary data needed to linearize the underlying discretization on the finer space V(h,p); thereby, only a linear system of equations is solved on the richer space V(h,p). Numerical experiments confirming the theoretical results are presented. |
| first_indexed | 2025-11-14T18:15:25Z |
| format | Article |
| id | nottingham-1481 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:15:25Z |
| publishDate | 2011 |
| publisher | Wiley-VCH |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-14812020-05-04T20:23:47Z https://eprints.nottingham.ac.uk/1481/ Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs Congreve, Scott Houston, Paul Wihler, Thomas P. In this article we develop the a priori error analysis of so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical approximation of strongly monotone second-order quasilinear partial differential equations. In this setting, the fully nonlinear problem is first approximated on a coarse finite element space V(H,P). The resulting `coarse' numerical solution is then exploited to provide the necessary data needed to linearize the underlying discretization on the finer space V(h,p); thereby, only a linear system of equations is solved on the richer space V(h,p). Numerical experiments confirming the theoretical results are presented. Wiley-VCH 2011 Article PeerReviewed Congreve, Scott, Houston, Paul and Wihler, Thomas P. (2011) Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs. Proceedings in Applied Mathematics and Mechanics, 11 (1). pp. 3-6. ISSN 1617-7061 http://onlinelibrary.wiley.com/doi/10.1002/pamm.201110002/pdf doi:10.1002/pamm.201110002 doi:10.1002/pamm.201110002 |
| spellingShingle | Congreve, Scott Houston, Paul Wihler, Thomas P. Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs |
| title | Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs |
| title_full | Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs |
| title_fullStr | Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs |
| title_full_unstemmed | Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs |
| title_short | Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs |
| title_sort | two-grid hp-version dgfems for strongly monotone second-order quasilinear elliptic pdes |
| url | https://eprints.nottingham.ac.uk/1481/ https://eprints.nottingham.ac.uk/1481/ https://eprints.nottingham.ac.uk/1481/ |