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

Applications of Mathematics (2017)

  • Volume: 62, Issue: 4, page 377-403
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Zhou, Guanyu, Kashiwabara, Takahito, and Oikawa, Issei. "A penalty method for the time-dependent Stokes problem with the slip boundary condition and its finite element approximation." Applications of Mathematics 62.4 (2017): 377-403. <http://eudml.org/doc/294129>.

@article{Zhou2017,
abstract = {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.},
author = {Zhou, Guanyu, Kashiwabara, Takahito, Oikawa, Issei},
journal = {Applications of Mathematics},
keywords = {penalty method; Stokes problem; finite element method; error estimate},
language = {eng},
number = {4},
pages = {377-403},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A penalty method for the time-dependent Stokes problem with the slip boundary condition and its finite element approximation},
url = {http://eudml.org/doc/294129},
volume = {62},
year = {2017},
}

TY - JOUR
AU - Zhou, Guanyu
AU - Kashiwabara, Takahito
AU - Oikawa, Issei
TI - A penalty method for the time-dependent Stokes problem with the slip boundary condition and its finite element approximation
JO - Applications of Mathematics
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 4
SP - 377
EP - 403
AB - 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.
LA - eng
KW - penalty method; Stokes problem; finite element method; error estimate
UR - http://eudml.org/doc/294129
ER -

References

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