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
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.
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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