| Publikationstyp: | Beitrag in wissenschaftlicher Zeitschrift |
| Art der Begutachtung: | Peer review (Publikation) |
| Titel: | Adaptive pseudo-transient-continuation-Galerkin methods for semilinear elliptic partial differential equations |
| Autor/-in: | Amrein, Mario Wihler, Thomas P. |
| DOI: | 10.1002/num.22177 |
| Erschienen in: | Numerical Methods for Partial Differential Equations |
| Band(Heft): | 33 |
| Heft: | 6 |
| Erscheinungsdatum: | 2017 |
| Verlag / Hrsg. Institution: | Wiley |
| ISSN: | 0749-159X 1098-2426 |
| Sprache: | Englisch |
| Schlagwörter: | Dynamical system; Steady states |
| Fachgebiet (DDC): | 510: Mathematik |
| Zusammenfassung: | 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 |
| Volltext Version: | Publizierte Version |
| Lizenz (gemäss Verlagsvertrag): | Lizenz gemäss Verlagsvertrag |
| Departement: | School of Management and Law |
| Organisationseinheit: | Institut für Risk & Insurance (IRI) |
| Enthalten in den Sammlungen: | 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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