Penalty Method for the Stationary Navier–Stokes Problems Under the Slip Boundary Condition

Guanyu Zhou, Takahito Kashiwabara, Issei Oikawa

研究成果: Article査読

8 被引用数 (Scopus)

抄録

We consider the penalty method for the stationary Navier–Stokes equations with the slip boundary condition. The well-posedness and the regularity theorem of the penalty problem are investigated, and we obtain the optimal error estimate (Formula presented.) in (Formula presented.)-norm, where (Formula presented.) is the penalty parameter. We are concerned with the finite element approximation with the P1b / P1 element to the penalty problem. The well-posedness of discrete problem is proved. We obtain the error estimate (Formula presented.) for the non-reduced-integration scheme with (Formula presented.), and the reduced-integration scheme with (Formula presented.), where h is the discretization parameter and d is the spatial dimension. For the reduced-integration scheme with (Formula presented.), we prove the convergence order (Formula presented.). The theoretical results are verified by numerical experiments.

本文言語English
ページ(範囲)1-36
ページ数36
ジャーナルJournal of Scientific Computing
DOI
出版ステータスAccepted/In press - 2015 11 27

ASJC Scopus subject areas

  • Software
  • Computational Theory and Mathematics
  • Theoretical Computer Science
  • Engineering(all)

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