Analysis of Stabilized Finite Volume Method for the Transient Stokes Equations

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.