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

Houston, Paul; Wihler, Thomas (2018). An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems. Mathematics of computation, 87(314), pp. 2641-2674. American Mathematical Society 10.1090/mcom/3308

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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:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Wihler, Thomas

Subjects:

500 Science > 510 Mathematics

ISSN:

0025-5718

Publisher:

American Mathematical Society

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

22 May 2019 14:37

Last Modified:

24 Oct 2019 12:38

Publisher DOI:

10.1090/mcom/3308

BORIS DOI:

10.7892/boris.125543

URI:

https://boris.unibe.ch/id/eprint/125543

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