ANALYSIS OF A STABILIZED FINITE VOLUME METHOD FOR THE TRANSIENT STOKES EQUATIONS

作者：Shen Lihua^*; Li Jian; Chen Zhangxin

来源：International Journal of Numerical Analysis and Modeling, 2009, 6(3): 505-519.

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

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.

• 出版日期2009
• 单位宝鸡文理学院; 首都师范大学; 西安交通大学