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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 = {L. Shen, J. Li and Z. Chen}, 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 AU - L. Shen, J. Li & Z. Chen 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 and Z. Chen. (2009). 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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