A penalty method for the time-dependent Stokes problem with the slip boundary condition and its finite element approximation

Guanyu Zhou*, Takahito Kashiwabara, Issei Oikawa

*この研究の対応する著者

研究成果: Article査読

2 被引用数 (Scopus)

抄録

We consider the finite element method for the time-dependent Stokes problem with the slip boundary condition in a smooth domain. To avoid a variational crime of numerical computation, a penalty method is introduced, which also facilitates the numerical implementation. For the continuous problem, the convergence of the penalty method is investigated. Then we study the fully discretized finite element approximations for the penalty method with the P1/P1-stabilization or P1b/P1 element. For the discretization of the penalty term, we propose reduced and non-reduced integration schemes, and obtain an error estimate for velocity and pressure. The theoretical results are verified by numerical experiments.

本文言語English
ページ(範囲)377-403
ページ数27
ジャーナルApplications of Mathematics
62
4
DOI
出版ステータスPublished - 2017 8 1

ASJC Scopus subject areas

  • 応用数学

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