Fully discrete best-approximation-type estimates in L(I; L2(Ω)d) for finite element discretizations of the transient Stokes equations

Niklas Behringer, Boris Vexler, Dmitriy Leykekhman

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this article, we obtain an optimal best-approximation-type result for fully discrete approximations of the transient Stokes problem. For the time discretization, we use the discontinuous Galerkin method and for the spatial discretization we use standard finite elements for the Stokes problem satisfying the discrete inf-sup condition. The analysis uses the technique of discrete maximal parabolic regularity. The results require only natural assumptions on the data and do not assume any additional smoothness of the solutions.

Original languageEnglish
Pages (from-to)852-880
Number of pages29
JournalIMA Journal of Numerical Analysis
Volume43
Issue number2
DOIs
StatePublished - 1 Mar 2023

Keywords

  • a priori estimates
  • best approximation
  • discontinuous Galerkin method
  • finite elements
  • pointwise error estimates
  • transient Stokes

Fingerprint

Dive into the research topics of 'Fully discrete best-approximation-type estimates in L(I; L2(Ω)d) for finite element discretizations of the transient Stokes equations'. Together they form a unique fingerprint.

Cite this