Abstract

The main goal of the paper is to show new stability and localization results for the finite element solution of the Stokes system in $W^{1,\infty}$ and $L^\infty$ norms under standard assumptions on the finite element spaces on quasi-uniform meshes in two and three dimensions. Although interior error estimates are well-developed for the elliptic problem, they appear to be new for the Stokes system on unstructured meshes. To obtain these results we extend previously known stability estimates for the Stokes system using regularized Green's functions.

Keywords

  1. maximum norm
  2. finite element
  3. best approximation error estimates
  4. Stokes

MSC codes

  1. 65N30
  2. 65N15

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Information & Authors

Information

Published In

cover image SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Pages: 1531 - 1555
ISSN (online): 1095-7170

History

Submitted: 12 July 2019
Accepted: 13 February 2020
Published online: 20 May 2020

Keywords

  1. maximum norm
  2. finite element
  3. best approximation error estimates
  4. Stokes

MSC codes

  1. 65N30
  2. 65N15

Authors

Affiliations

Funding Information

Austrian Science Fund https://doi.org/10.13039/501100002428
Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659
National Science Foundation https://doi.org/10.13039/100000001 : DMS-1913133

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