A posteriori estimates for the two-step backward differentiation formula and discrete regularity for the time-dependent Stokes equations

Bänsch E, Brenner A (2019)

Publication Type: Journal article

Publication year: 2019

Journal

IMA Journal of Numerical Analysis Oxford University Press (OUP): Policy A - Oxford Open Option A

Book Volume: 39

Pages Range: 713-759

Journal Issue: 2

DOI: 10.1093/imanum/dry014

Abstract

We derive optimal order residual-based a posteriori error estimates for fully discrete finite element approximations to the time-dependent Stokes equations. The time discretization uses the two-step backward differentiation formula, and the space discretization is based on inf-sup stable pairs of finite elements, which are allowed to change with time. We show that the time error estimators are of optimal order. This proof of optimality uses time regularity of the semidiscrete (discrete in space) time-dependent Stokes equations. Computational examples are given to confirm the theoretical findings. For completeness, a priori estimates are also presented.

Authors with CRIS profile

Eberhard Bänsch Lehrstuhl für Angewandte Mathematik (Wissenschaftliches Rechnen) Andreas Brenner Lehrstuhl für Angewandte Mathematik (Wissenschaftliches Rechnen)

How to cite

APA:

Bänsch, E., & Brenner, A. (2019). A posteriori estimates for the two-step backward differentiation formula and discrete regularity for the time-dependent Stokes equations. IMA Journal of Numerical Analysis, 39(2), 713-759. https://doi.org/10.1093/imanum/dry014

MLA:

Bänsch, Eberhard, and Andreas Brenner. "A posteriori estimates for the two-step backward differentiation formula and discrete regularity for the time-dependent Stokes equations." IMA Journal of Numerical Analysis 39.2 (2019): 713-759.

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