An adaptive certified space-time reduced basis method for nonsmooth parabolic partial differential equations

Bernreuther, Marco; Volkwein, Stefan

An adaptive certified space-time reduced basis method for nonsmooth parabolic partial differential equations

Dateien

Bernreuther_2-nzqyelp0fc7e0.pdfGröße: 1.13 MBDownloads: 12

Datum

2024

Angaben zur Forschungsförderung

Deutsche Forschungsgemeinschaft (DFG): VO 1658/5-2

Open Access-Veröffentlichung

Open Access Hybrid

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

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.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Nonsmooth parabolic equations, Space-time discretization, Reduced basis, Discrete empirical interpolation, A-posteriori error estimation, Semismooth Newton

Zitieren

ISO 690

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/s10444-024-10137-4

BibTex

@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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