Unilateral problem for the Stokes equations: The well-posedness and finite element approximation

Norikazu Saito, Yoshiki Sugitani, Guanyu Zhou

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

We consider the stationary Stokes equations under a unilateral boundary condition of Signorini's type, which is one of artificial boundary conditions in flow problems. Well-posedness is discussed through its variational inequality formulation. We also consider the finite element approximation for a regularized penalty problem. The well-posedness, stability and error estimates of optimal order are established. The lack of a coupled Babuška and Brezzi's condition makes analysis difficult. We offer a new method of analysis. Particularly, our device to treat the pressure is novel and of some interest. Numerical examples are presented to validate our theoretical results.

Original languageEnglish
Pages (from-to)124-147
Number of pages24
JournalApplied Numerical Mathematics
Volume105
DOIs
Publication statusPublished - 2016 Jul 1
Externally publishedYes

Keywords

  • Finite element approximation
  • Stokes equations
  • Unilateral boundary condition

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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