无界区域上轴对称Stokes绕流的混合有限元方法

THE MIXED FINITE ELEMENT METHOD FOR AXISYMMETRIC STOKES FLOW ON UNBOUNDED DOMAINS

本文讨论无界区域上轴对称Stokes绕流边值问题的有限元近似解。为了克服边界无界性所带来的困难,本文将传统的分析方法与有限元法相结合,首先将问题化为一个等价的有界区域上的边值问题,然后用有限元方法求得这个等价问题的近似解。作为算例,本文计算了圆球的Stokes绕流,并给出其近似解的误差分析。

This paper deals with the finite element approximation of the axisymmetric Stokes flow on unbounded domains. In order to overcome the difficulties caused by the unbounded domains, the finite element method is combined with the classical analytical method and the equivalent boundary value problem on bounded domains is obtained, which is solved numerically by the finite element techneque. As an example, the Stokes flow around the sphere is calculated and the error estimate of the approximate solutions is given.