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https://doi.org/10.21256/zhaw-3454| Publication type: | Article in scientific journal |
| Type of review: | Peer review (publication) |
| Title: | An adaptive space-time Newton–Galerkin approach for semilinear singularly perturbed parabolic evolution equations |
| Authors: | Amrein, Mario Wihler, Thomas P. |
| DOI: | 10.21256/zhaw-3454 10.1093/imanum/drw049 |
| Published in: | The IMA Journal of Numerical Analysis |
| Volume(Issue): | 37 |
| Issue: | 4 |
| Page(s): | 2004 |
| Pages to: | 2019 |
| Issue Date: | 2016 |
| Publisher / Ed. Institution: | Oxford University Press |
| ISSN: | 0272-4979 1464-3642 |
| Language: | English |
| Subject (DDC): | 510: Mathematics |
| Abstract: | In this article, we develop an adaptive procedure for the numerical solution of semilinear parabolic problems with possible singular perturbations. Our approach combines a linearization technique using Newton’s method with an adaptive discretization – which is based on a spatial finite element method and the backward Euler time-stepping scheme – of the resulting sequence of linear problems. Upon deriving a robust a posteriori error analysis, we design a fully adaptive Newton-Galerkin time-stepping algorithm. Numerical experiments underline the robustness and reliability of the proposed approach for various examples. |
| Further description: | Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch) |
| URI: | https://digitalcollection.zhaw.ch/handle/11475/13223 |
| 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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| File | Description | Size | Format | |
|---|---|---|---|---|
| Time-Adaptive_Paper_.pdf | 414.9 kB | Adobe PDF |  View/Open |
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Amrein, M., & Wihler, T. P. (2016). An adaptive space-time Newton–Galerkin approach for semilinear singularly perturbed parabolic evolution equations. The IMA Journal of Numerical Analysis, 37(4), 2004–2019. https://doi.org/10.21256/zhaw-3454
Amrein, M. and Wihler, T.P. (2016) ‘An adaptive space-time Newton–Galerkin approach for semilinear singularly perturbed parabolic evolution equations’, The IMA Journal of Numerical Analysis, 37(4), pp. 2004–2019. Available at: https://doi.org/10.21256/zhaw-3454.
M. Amrein and T. P. Wihler, “An adaptive space-time Newton–Galerkin approach for semilinear singularly perturbed parabolic evolution equations,” The IMA Journal of Numerical Analysis, vol. 37, no. 4, pp. 2004–2019, 2016, doi: 10.21256/zhaw-3454.
AMREIN, Mario und Thomas P. WIHLER, 2016. An adaptive space-time Newton–Galerkin approach for semilinear singularly perturbed parabolic evolution equations. The IMA Journal of Numerical Analysis. 2016. Bd. 37, Nr. 4, S. 2004–2019. DOI 10.21256/zhaw-3454
Amrein, Mario, and Thomas P. Wihler. 2016. “An Adaptive Space-Time Newton–Galerkin Approach for Semilinear Singularly Perturbed Parabolic Evolution Equations.” The IMA Journal of Numerical Analysis 37 (4): 2004–19. https://doi.org/10.21256/zhaw-3454.
Amrein, Mario, and Thomas P. Wihler. “An Adaptive Space-Time Newton–Galerkin Approach for Semilinear Singularly Perturbed Parabolic Evolution Equations.” The IMA Journal of Numerical Analysis, vol. 37, no. 4, 2016, pp. 2004–19, https://doi.org/10.21256/zhaw-3454.
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