A new stabilized finite volume method for the stationary Stokes equations

作者：Li Jian; Chen Zhangxin^*

来源：Advances in Computational Mathematics, 2009, 30(2): 141-152.

DOI：10.1007/s10444-007-9060-5

• Stokes equations
• Finite element method
• Finite volume method
• Inf-sup condition
• Error estimate

In this paper we develop and study a new stabilized finite volume method for the two-dimensional Stokes equations. This method is based on a local Gauss integration technique and the conforming elements of the lowest-equal order pair (i.e., the P (1)-P (1) pair). After a relationship between this method and a stabilized finite element method is established, 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2009-2
• 单位西安交通大学