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

Takahito Kashiwabara, Issei Oikawa, Guanyu Zhou

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9 Citations (Scopus)


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
Publication statusAccepted/In press - 2016 Jan 23


ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

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