An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems
In this paper we develop an hp-adaptive procedure for the numerical solution of general second-order semilinear elliptic boundary value problems, with possible singular perturbation. Our approach combines both adaptive Newton schemes and an hp-version adaptive discontinuous Galerkin finite element d...
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| Format: | Article |
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American Mathematical Society
2018
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| Online Access: | https://eprints.nottingham.ac.uk/43760/ |
| _version_ | 1848796762402193408 |
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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 paper we develop an hp-adaptive procedure for the numerical solution of general second-order semilinear elliptic boundary value problems, with possible singular perturbation. Our approach combines both adaptive Newton schemes and an hp-version adaptive discontinuous Galerkin finite element discretisation, which, in turn, is based on a robust hp-version a posteriori residual analysis. Numerical experiments underline the robustness and reliability of the proposed approach for various examples. |
| first_indexed | 2025-11-14T19:53:08Z |
| format | Article |
| id | nottingham-43760 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:53:08Z |
| publishDate | 2018 |
| publisher | American Mathematical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-437602020-05-04T19:28:12Z https://eprints.nottingham.ac.uk/43760/ An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems Houston, Paul Wihler, Thomas P. In this paper we develop an hp-adaptive procedure for the numerical solution of general second-order semilinear elliptic boundary value problems, with possible singular perturbation. Our approach combines both adaptive Newton schemes and an hp-version adaptive discontinuous Galerkin finite element discretisation, which, in turn, is based on a robust hp-version a posteriori residual analysis. Numerical experiments underline the robustness and reliability of the proposed approach for various examples. American Mathematical Society 2018-01-24 Article PeerReviewed Houston, Paul and Wihler, Thomas P. (2018) An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems. Mathematics of Computation . ISSN 1088-6842 Newton method Semilinear elliptic problems Adaptive finite element methods Discontinuous Galerkin methods hp-adaptivity http://www.ams.org/journals/mcom/0000-000-00/S0025-5718-2018-03308-7/home.html doi:10.1090/mcom/3308 doi:10.1090/mcom/3308 |
| spellingShingle | Newton method Semilinear elliptic problems Adaptive finite element methods Discontinuous Galerkin methods hp-adaptivity Houston, Paul Wihler, Thomas P. An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems |
| title | An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems |
| title_full | An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems |
| title_fullStr | An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems |
| title_full_unstemmed | An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems |
| title_short | An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems |
| title_sort | hp-adaptive newton-discontinuous-galerkin finite element approach for semilinear elliptic boundary value problems |
| topic | Newton method Semilinear elliptic problems Adaptive finite element methods Discontinuous Galerkin methods hp-adaptivity |
| url | https://eprints.nottingham.ac.uk/43760/ https://eprints.nottingham.ac.uk/43760/ https://eprints.nottingham.ac.uk/43760/ |