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

Amrein, Mario; Melenk, Jens M.; Wihler, Thomas P.

doi:10.1002/mma.4113

Publication type:	Article in scientific journal
Type of review:	Peer review (publication)
Title:	An hp-adaptive Newton-Galerkin finite element procedure for semilinear boundary value problems
Authors:	Amrein, Mario Melenk, Jens M. Wihler, Thomas P.
et. al:	No
DOI:	10.1002/mma.4113
Published in:	Mathematical Methods in the Applied Sciences
Volume(Issue):	40
Issue:	6
Page(s):	1973
Pages to:	1985
Issue Date:	2-Aug-2016
Publisher / Ed. Institution:	Wiley
ISSN:	0170-4214
Language:	English
Subjects:	Adaptive Newton method; Adaptive finite element method; Semilinear elliptic problem; Singularly perturbed problem
Subject (DDC):	510: Mathematics
Abstract:	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.
URI:	https://digitalcollection.zhaw.ch/handle/11475/17927
Fulltext version:	Published version
License (according to publishing contract):	Licence according to publishing contract
Departement:	School of Management and Law
Organisational Unit:	Institute for Risk & Insurance (IRI)
Appears in collections:	Publikationen School of Management and Law

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Amrein, M., Melenk, J. M., & Wihler, T. P. (2016). An hp-adaptive Newton-Galerkin finite element procedure for semilinear boundary value problems. Mathematical Methods in the Applied Sciences, 40(6), 1973–1985. https://doi.org/10.1002/mma.4113

Amrein, M., Melenk, J.M. and Wihler, T.P. (2016) ‘An hp-adaptive Newton-Galerkin finite element procedure for semilinear boundary value problems’, Mathematical Methods in the Applied Sciences, 40(6), pp. 1973–1985. Available at: https://doi.org/10.1002/mma.4113.

M. Amrein, J. M. Melenk, and T. P. Wihler, “An hp-adaptive Newton-Galerkin finite element procedure for semilinear boundary value problems,” Mathematical Methods in the Applied Sciences, vol. 40, no. 6, pp. 1973–1985, Aug. 2016, doi: 10.1002/mma.4113.

AMREIN, Mario, Jens M. MELENK und Thomas P. WIHLER, 2016. An hp-adaptive Newton-Galerkin finite element procedure for semilinear boundary value problems. Mathematical Methods in the Applied Sciences. 2 August 2016. Bd. 40, Nr. 6, S. 1973–1985. DOI 10.1002/mma.4113

Amrein, Mario, Jens M. Melenk, and Thomas P. Wihler. 2016. “An Hp-Adaptive Newton-Galerkin Finite Element Procedure for Semilinear Boundary Value Problems.” Mathematical Methods in the Applied Sciences 40 (6): 1973–85. https://doi.org/10.1002/mma.4113.

Amrein, Mario, et al. “An Hp-Adaptive Newton-Galerkin Finite Element Procedure for Semilinear Boundary Value Problems.” Mathematical Methods in the Applied Sciences, vol. 40, no. 6, Aug. 2016, pp. 1973–85, https://doi.org/10.1002/mma.4113.