Volume 6, Issue 3
Analysis of Stabilized Finite Volume Method for the Transient Stokes Equations

L. Shen, J. Li & Z. Chen

Int. J. Numer. Anal. Mod., 6 (2009), pp. 505-519.

Published online: 2009-06

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  • Abstract

This paper is concerned with the development and study of a stabilized finite volume method for the transient Stokes problem in two and three dimensions. The stabilization is based on two local Gauss integrals and is parameter-free. The analysis is based on a relationship between this new finite volume method and a stabilized finite element method using the lowest equal-order pair (i.e., the $P_1$-$P_1$ pair). An error estimate of optimal order in the $H^1$-norm for velocity and an estimate in the $L^2$-norm for pressure are obtained. An optimal error estimate in the $L^2$-norm for the velocity is derived under an additional assumption on the body force.

  • Keywords

Transient Stokes equations, stabilized finite volume method, inf-sup condition, local Gauss integrals, optimal error estimate, stability.

  • AMS Subject Headings

35Q10, 65N30, 76D05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-6-505, author = {}, title = {Analysis of Stabilized Finite Volume Method for the Transient Stokes Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2009}, volume = {6}, number = {3}, pages = {505--519}, abstract = {

This paper is concerned with the development and study of a stabilized finite volume method for the transient Stokes problem in two and three dimensions. The stabilization is based on two local Gauss integrals and is parameter-free. The analysis is based on a relationship between this new finite volume method and a stabilized finite element method using the lowest equal-order pair (i.e., the $P_1$-$P_1$ pair). An error estimate of optimal order in the $H^1$-norm for velocity and an estimate in the $L^2$-norm for pressure are obtained. An optimal error estimate in the $L^2$-norm for the velocity is derived under an additional assumption on the body force.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/781.html} }
TY - JOUR T1 - Analysis of Stabilized Finite Volume Method for the Transient Stokes Equations JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 505 EP - 519 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/781.html KW - Transient Stokes equations, stabilized finite volume method, inf-sup condition, local Gauss integrals, optimal error estimate, stability. AB -

This paper is concerned with the development and study of a stabilized finite volume method for the transient Stokes problem in two and three dimensions. The stabilization is based on two local Gauss integrals and is parameter-free. The analysis is based on a relationship between this new finite volume method and a stabilized finite element method using the lowest equal-order pair (i.e., the $P_1$-$P_1$ pair). An error estimate of optimal order in the $H^1$-norm for velocity and an estimate in the $L^2$-norm for pressure are obtained. An optimal error estimate in the $L^2$-norm for the velocity is derived under an additional assumption on the body force.

L. Shen, J. Li & Z. Chen. (1970). Analysis of Stabilized Finite Volume Method for the Transient Stokes Equations. International Journal of Numerical Analysis and Modeling. 6 (3). 505-519. doi:
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