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An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems

Houston, Paul; Wihler, Thomas P.

Authors

PAUL HOUSTON paul.houston@nottingham.ac.uk
Professor of Computational and Applied Maths

Thomas P. Wihler wihler@math.unibe.ch



Abstract

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.

Citation

Houston, P., & Wihler, T. P. (in press). An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems. Mathematics of Computation, https://doi.org/10.1090/mcom/3308

Journal Article Type Article
Acceptance Date Jun 25, 2017
Online Publication Date Jan 24, 2018
Deposit Date Jun 27, 2017
Publicly Available Date Jan 24, 2018
Journal Mathematics of Computation
Print ISSN 0025-5718
Electronic ISSN 1088-6842
Publisher American Mathematical Society
Peer Reviewed Peer Reviewed
DOI https://doi.org/10.1090/mcom/3308
Keywords Newton method, Semilinear elliptic problems, Adaptive finite element methods, Discontinuous Galerkin methods, hp-adaptivity
Public URL http://eprints.nottingham.ac.uk/id/eprint/43760
Publisher URL http://www.ams.org/journals/mcom/0000-000-00/S0025-5718-2018-03308-7/home.html
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf
Additional Information First published in Mathematics of Computation, 24 January 2018, by the American Mathematical Society.

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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