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

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

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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.

Item Type: Article
Additional Information: First published in Mathematics of Computation, 24 January 2018, by the American Mathematical Society.
Keywords: Newton method, Semilinear elliptic problems, Adaptive finite element methods, Discontinuous Galerkin methods, hp-adaptivity
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1090/mcom/3308
Depositing User: Houston, Paul
Date Deposited: 27 Jun 2017 08:34
Last Modified: 03 Feb 2018 20:19
URI: http://eprints.nottingham.ac.uk/id/eprint/43760

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