Publikation: An adaptive certified space-time reduced basis method for nonsmooth parabolic partial differential equations
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2024
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Deutsche Forschungsgemeinschaft (DFG): VO 1658/5-2
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Advances in Computational Mathematics. Springer. 2024, 50(3), 48. ISSN 1019-7168. eISSN 1572-9044. Verfügbar unter: doi: 10.1007/s10444-024-10137-4
Zusammenfassung
In this paper, a nonsmooth semilinear parabolic partial differential equation (PDE) is considered. For a reduced basis (RB) approach, a space-time formulation is used to develop a certified a-posteriori error estimator. This error estimator is adopted to the presence of the discrete empirical interpolation method (DEIM) as approximation technique for the nonsmoothness. The separability of the estimated error into an RB and a DEIM part then guides the development of an adaptive RB-DEIM algorithm, combining both offline phases into one. Numerical experiments show the capabilities of this novel approach in comparison with classical RB and RB-DEIM approaches.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
Schlagwörter
Nonsmooth parabolic equations, Space-time discretization, Reduced basis, Discrete empirical interpolation, A-posteriori error estimation, Semismooth Newton
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BERNREUTHER, Marco, Stefan VOLKWEIN, 2024. An adaptive certified space-time reduced basis method for nonsmooth parabolic partial differential equations. In: Advances in Computational Mathematics. Springer. 2024, 50(3), 48. ISSN 1019-7168. eISSN 1572-9044. Verfügbar unter: doi: 10.1007/s10444-024-10137-4BibTex
@article{Bernreuther2024-06adapt-70690,
year={2024},
doi={10.1007/s10444-024-10137-4},
title={An adaptive certified space-time reduced basis method for nonsmooth parabolic partial differential equations},
number={3},
volume={50},
issn={1019-7168},
journal={Advances in Computational Mathematics},
author={Bernreuther, Marco and Volkwein, Stefan},
note={Article Number: 48}
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