An $hp$-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems
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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.References
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Additional Information
- Paul Houston
- Affiliation: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom
- MR Author ID: 635107
- Email: Paul.Houston@nottingham.ac.uk
- Thomas P. Wihler
- Affiliation: Mathematics Institute, University of Bern, CH-3012 Bern, Switzerland
- MR Author ID: 662940
- ORCID: 0000-0003-1232-0637
- Email: wihler@math.unibe.ch
- Received by editor(s): July 22, 2016
- Received by editor(s) in revised form: April 7, 2017, and May 31, 2017
- Published electronically: January 24, 2018
- Additional Notes: The second author acknowledges the support of the Swiss National Science Foundation (SNF), Grant No. 200021-162990
- © Copyright 2018 American Mathematical Society
- Journal: Math. Comp. 87 (2018), 2641-2674
- MSC (2010): Primary 65N30
- DOI: https://doi.org/10.1090/mcom/3308
- MathSciNet review: 3834680