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

Houston, Paul; Wihler, Thomas P.

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: https://nottingham-repository.worktribe.com/output/906846
• Publisher URL: http://www.ams.org/journals/mcom/0000-000-00/S0025-5718-2018-03308-7/home.html
• Additional Information: First published in Mathematics of Computation, 24 January 2018, by the American Mathematical Society.