An adaptive space-time Newton-Galerkin approach for semilinear singularly perturbed parabolic evolution equations

Amrein, Mario; Wihler, Thomas (2017). An adaptive space-time Newton-Galerkin approach for semilinear singularly perturbed parabolic evolution equations. IMA journal of numerical analysis, 37(4), pp. 2004-2019. Oxford University Press 10.1093/imanum/drw049

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In this article, we develop an adaptive procedure for the numerical solution of semilinear parabolic problems with possible singular perturbations. Our approach combines a linearization technique using Newton’s method with an adaptive discretization—which is based on a spatial finite element method and the backward Euler time-stepping scheme—of the resulting sequence of linear problems. Upon deriving a robust a posteriori error analysis, we design a fully adaptive Newton–Galerkin time-stepping algorithm. 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:

0272-4979

Publisher:

Oxford University Press

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

17 Apr 2018 09:17

Last Modified:

17 Apr 2018 09:17

Publisher DOI:

10.1093/imanum/drw049

BORIS DOI:

10.7892/boris.109177

URI:

https://boris.unibe.ch/id/eprint/109177

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