Penalty method with P1/P1 finite element approximation for the Stokes equations under the slip boundary condition

Takahito Kashiwabara, Issei Oikawa, Guanyu Zhou

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We consider the P1/P1 or P1b/P1 finite element approximations to the Stokes equations in a bounded smooth domain subject to the slip boundary condition. A penalty method is applied to address the essential boundary condition (Formula presented.) on (Formula presented.), which avoids a variational crime and simultaneously facilitates the numerical implementation. We give (Formula presented.)-error estimate for velocity and pressure in the energy norm, where h and (Formula presented.) denote the discretization parameter and the penalty parameter, respectively. In the two-dimensional case, it is improved to (Formula presented.) by applying reduced-order numerical integration to the penalty term. The theoretical results are confirmed by numerical experiments.

Original languageEnglish
Pages (from-to)1-36
Number of pages36
JournalNumerische Mathematik
DOIs
Publication statusAccepted/In press - 2016 Jan 23

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Slip Boundary Condition
Penalty Method
Stokes Equations
Finite Element Approximation
Boundary conditions
Crime
Penalty
Experiments
Numerical integration
Error Estimates
Discretization
Numerical Experiment
Denote
Norm
Term
Energy

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Cite this

Penalty method with P1/P1 finite element approximation for the Stokes equations under the slip boundary condition. / Kashiwabara, Takahito; Oikawa, Issei; Zhou, Guanyu.

In: Numerische Mathematik, 23.01.2016, p. 1-36.

Research output: Contribution to journalArticle

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