A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

Marc Gerritsma, Pavel Bochev

Research output: Contribution to journalArticleScientificpeer-review

9 Citations (Scopus)

Abstract

Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity-vorticity-pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximated by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. We also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.

Original languageEnglish
Pages (from-to)2285-2300
Number of pages16
JournalComputers & Mathematics with Applications
Volume71
Issue number11
DOIs
Publication statusPublished - 1 Jun 2016
EventConference on Advances in Scientific Computing and Applied Mathematics - Las Vegas, United States
Duration: 9 Oct 201512 Oct 2016
http://www.csm.ornl.gov/workshops/ASCAM/index.html

Keywords

  • Least-squares
  • Mass conservation
  • Mimetic methods
  • Spectral element method

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