A priori error analysis for finite element approximations of the Stokes problem on dynamic meshes

Brenner A, BĂ€nsch E, Bause M (2014)

Publication Type: Journal article, Original article

Publication year: 2014

Journal

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

Publisher: Oxford University Press (OUP): Policy A - Oxford Open Option A

Book Volume: 34

Pages Range: 123-146

Journal Issue: 1

DOI: 10.1093/imanum/drt001

Abstract

In this article we study finite element approximations of the time-dependent Stokes system on dynamically changing meshes. Applying the backward Euler method for time discretization we use the discrete Helmholtz or Stokes projection to evaluate the solution at time tn−1 on the new spatial mesh at time tn. The theoretical results consist of a priori error estimates that show a dependence on the time step size not better than đ’Ș(1/Δt). These surprisingly pessimistic upper bounds are complemented by numerical examples giving evidence for a negative convergence rate, at least for a large range of time step sizes, and in this sense backing our theory. These observations imply that using adaptive meshes for incompressible flow problems is delicate and requires further investigation.

Authors with CRIS profile

Andreas Brenner Lehrstuhl fĂŒr Angewandte Mathematik (Wissenschaftliches Rechnen) Eberhard BĂ€nsch Lehrstuhl fĂŒr Angewandte Mathematik (Wissenschaftliches Rechnen)

How to cite

APA:

Brenner, A., Bänsch, E., & Bause, M. (2014). A priori error analysis for finite element approximations of the Stokes problem on dynamic meshes. IMA Journal of Numerical Analysis, 34(1), 123-146. https://doi.org/10.1093/imanum/drt001

MLA:

Brenner, Andreas, Eberhard Bänsch, and Markus Bause. "A priori error analysis for finite element approximations of the Stokes problem on dynamic meshes." IMA Journal of Numerical Analysis 34.1 (2014): 123-146.

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