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

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Date

2022

Publication type

Preprint

Publication status

Published

Abstract

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.

Subject (DDC)

510 Mathematics

Keywords

Nonsmooth parabolic equations, space-time discretization, reduced basis, discrete empirical interpolation, a-posteriori error estimation, semismooth Newton

Cite This

ISO 690

BERNREUTHER, 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@unpublished{Bernreuther2022-12-28T08:41:11Zadapt-59662,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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