定常Navier-Stokes方程两层稳定有限元方法  

A TWO-LEVEL STABILIZED FINITE ELEMENT METHOD FOR STATIONARY NAVIER-STOKES EQUATIONS

作　　者：杨建宏[1] 

机构地区：[1]宝鸡文理学院数学系,宝鸡721013

出　　处：《高等学校计算数学学报》2011年第3期225-234,共10页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(11071193);宝鸡文理学院重点科研项目(ZK10113)

摘　　要：构造高效率、高精度又便于计算机实现的数值计算方法是科学计算的核心内容．N—S方程是不可压缩流体的控制方程，对它的求解方法的研究一直受到国内外众多有限元专家学者的关注．众所周知，利用有限元方法求解N—S方程，关于速度和压力的有限元对必须满足inf-sup条件，即要求速度分片多项式次数比压力多项式次数高，而且在具体计算中需要采用不同的两套网格．显然，这增加了计算的难度和工作量．In this paper, we consider a two-level stabilized finite element method for the two-dimensional stationary Navier-Stokes equation approximated by the lowest equal-order elements which do not satisfy the inf-sup condition. The two- level method consists of solving a small non-linear system on the coarse mesh and then solving a Stokes equation on the fine mesh. The error analysis shows that the two-level stabilized finite element method has the same convergence rate as the usual stabilized finite element solution on a fine mesh with the relation h = O（H^2）. Moreover, numerical analysis completely confirms the theoretical results. Therefore, this method presented in this paper is of practical importance in scientific computation.

关 键 词：STOKES方程 有限元方法 数值计算方法 INF-SUP条件 稳定 定常 不可压缩流体 求解方法 

分 类 号：O241.1[理学—计算数学]