Analysis on a Finite Volume Element Method for Stokes Problems  

作　　者：Hong-xing Rui 

机构地区：[1]School of Mathematics and Systems Science, Shandong University, Jinan 250100, China

出　　处：《Acta Mathematicae Applicatae Sinica》2005年第3期359-372,共14页应用数学学报（英文版）

基　　金：Supported by the Natural Science Foundation of China （No.10471079, 10071044） and the Research Fund of Doctoral Program of High Education by State Education Ministry of China.

摘　　要：Finite volume element method for the Stokes problem is considered. We use a conforming piecewise linear function on a fine grid for velocity and piecewise constant element on a coarse grid for pressure. For general triangulation we prove the equivalence of the finite volume element method and a saddle-point problem, the inf-sup condition and the uniqueness of the approximation solution. We also give the optimal order H^1 norm error estimate. For two widely used dual meshes we give the L^2 norm error estimates, which is optimal in one case and quasi-optimal in another ease. Finally we give a numerical example.Finite volume element method for the Stokes problem is considered. We use a conforming piecewise linear function on a fine grid for velocity and piecewise constant element on a coarse grid for pressure. For general triangulation we prove the equivalence of the finite volume element method and a saddle-point problem, the inf-sup condition and the uniqueness of the approximation solution. We also give the optimal order H^1 norm error estimate. For two widely used dual meshes we give the L^2 norm error estimates, which is optimal in one case and quasi-optimal in another ease. Finally we give a numerical example.

关 键 词：Finite volume element Stokes problem numerical analysis 

分 类 号：O241.82[理学—计算数学]