An hp-adaptive Newton-Galerkin finite element procedure for semilinear boundary value problems

Amrein, Mario; Melenk, Jens Markus; Wihler, Thomas (2017). An hp-adaptive Newton-Galerkin finite element procedure for semilinear boundary value problems. Mathematical methods in the applied sciences, 40(6), pp. 1973-1985. Wiley 10.1002/mma.4113

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In this paper, we develop an hp-adaptive procedure for the numerical solution of general, semilinear elliptic boundary value problems in 1d, with possible singular perturbations. Our approach combines both a prediction-type adaptive Newton method and an hp-version adaptive finite element discretization (based on a robust a posteriori residual analysis), thereby leading to a fully hp-adaptive Newton–Galerkin scheme. 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:

Amrein, Mario and Wihler, Thomas

Subjects:

500 Science > 510 Mathematics

ISSN:

0170-4214

Publisher:

Wiley

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

17 Apr 2018 09:09

Last Modified:

17 Apr 2018 09:09

Publisher DOI:

10.1002/mma.4113

BORIS DOI:

10.7892/boris.109182

URI:

https://boris.unibe.ch/id/eprint/109182

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