Analysis of Stabilized Finite Volume Method for the Transient Stokes Equations
Year: 2009
International Journal of Numerical Analysis and Modeling, Vol. 6 (2009), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-IJNAM-781
International Journal of Numerical Analysis and Modeling, Vol. 6 (2009), Iss. 3 : pp. 505–519
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Transient Stokes equations stabilized finite volume method inf-sup condition local Gauss integrals optimal error estimate stability.