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.
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