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

Amrein, Mario; Wihler, Thomas P.

doi:10.1002/num.22177

Publication type:	Article in scientific journal
Type of review:	Peer review (publication)
Title:	Adaptive pseudo-transient-continuation-Galerkin methods for semilinear elliptic partial differential equations
Authors:	Amrein, Mario Wihler, Thomas P.
DOI:	10.1002/num.22177
Published in:	Numerical Methods for Partial Differential Equations
Volume(Issue):	33
Issue:	6
Issue Date:	2017
Publisher / Ed. Institution:	Wiley
ISSN:	0749-159X 1098-2426
Language:	English
Subjects:	Dynamical system; Steady states
Subject (DDC):	510: Mathematics
Abstract:	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.
URI:	https://digitalcollection.zhaw.ch/handle/11475/11154
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., & Wihler, T. P. (2017). Adaptive pseudo-transient-continuation-Galerkin methods for semilinear elliptic partial differential equations. Numerical Methods for Partial Differential Equations, 33(6). https://doi.org/10.1002/num.22177

Amrein, M. and Wihler, T.P. (2017) ‘Adaptive pseudo-transient-continuation-Galerkin methods for semilinear elliptic partial differential equations’, Numerical Methods for Partial Differential Equations, 33(6). Available at: https://doi.org/10.1002/num.22177.

M. Amrein and T. P. Wihler, “Adaptive pseudo-transient-continuation-Galerkin methods for semilinear elliptic partial differential equations,” Numerical Methods for Partial Differential Equations, vol. 33, no. 6, 2017, doi: 10.1002/num.22177.

AMREIN, Mario und Thomas P. WIHLER, 2017. Adaptive pseudo-transient-continuation-Galerkin methods for semilinear elliptic partial differential equations. Numerical Methods for Partial Differential Equations. 2017. Bd. 33, Nr. 6. DOI 10.1002/num.22177

Amrein, Mario, and Thomas P. Wihler. 2017. “Adaptive Pseudo-Transient-Continuation-Galerkin Methods for Semilinear Elliptic Partial Differential Equations.” Numerical Methods for Partial Differential Equations 33 (6). https://doi.org/10.1002/num.22177.

Amrein, Mario, and Thomas P. Wihler. “Adaptive Pseudo-Transient-Continuation-Galerkin Methods for Semilinear Elliptic Partial Differential Equations.” Numerical Methods for Partial Differential Equations, vol. 33, no. 6, 2017, https://doi.org/10.1002/num.22177.