Adaptive pseudo-transient-continuation-Galerkin methods for semilinear elliptic partial differential equations

Amrein, Mario; Wihler, Thomas (2017). Adaptive pseudo-transient-continuation-Galerkin methods for semilinear elliptic partial differential equations. Numerical methods for partial differential equations, 33(6), pp. 2005-2022. Wiley 10.1002/num.22177

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In this article, we investigate the application of pseudo-transient-continuation (PTC) schemes for the numerical solution of semilinear elliptic partial differential equations, with possible singular perturbations. We will outline a residual reduction analysis within the framework of general Hilbert spaces, and, subsequently, use the PTC-methodology in the context of finite element discretizations of semilinear boundary value problems. Our approach combines both a prediction-type PTC-method (for infinite dimensional problems) and an adaptive finite element discretization (based on a robust a posteriori residual analysis), thereby leading to a fully adaptive PTC -Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for different 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:

0749-159X

Publisher:

Wiley

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

17 Apr 2018 09:36

Last Modified:

25 Oct 2019 20:50

Publisher DOI:

10.1002/num.22177

BORIS DOI:

10.7892/boris.109178

URI:

https://boris.unibe.ch/id/eprint/109178

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