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

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2022
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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.

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Fachgebiet (DDC)
510 Mathematik
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Nonsmooth parabolic equations, space-time discretization, reduced basis, discrete empirical interpolation, a-posteriori error estimation, semismooth Newton
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ISO 690BERNREUTHER, Marco, Stefan VOLKWEIN, 2022. An adaptive certified space-time reduced basis method for nonsmooth parabolic partial differential equations
BibTex
@unpublished{Bernreuther2022-12-28T08:41:11Zadapt-59662,
  year={2022},
  title={An adaptive certified space-time reduced basis method for nonsmooth parabolic partial differential equations},
  author={Bernreuther, Marco and Volkwein, Stefan}
}
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