@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} }