无界区域上Stokes问题的自然边界元与有限元耦合法

The Coupling of Natural BEM and FEM for Stokes Problem on Unbounded Domain

§1.引言 对于用有限元方法求解平面有界区域上的Stokes问题,国内外已有大量工作,例如可见[2]、[9]及其所引文献.但对无界区域上的这一问题,由于区域的无界性给有限元方法带来了困难,边界元方法及边界元与有限元的耦合法便显示其优越性.本文提出用自然边界元与有限元的耦合法求解无界区域上的Stokes问题.这一耦合法早在作者以前的工作中被应用于求解调和问题、重调和问题和平面弹性问题。

In this paper, the coupling of the Natural boundary element method and the finite ele-ment method for Stokes problem on an unbounded domain is considered. In order to overcomethe difficulty caused by infinity of the domain, the Natural boundary reduction is applied toreduce the problem into an equivalent boundary value problem on a bounded domain. This newproblem is solved numerically by coupling the boundary element method with the mixed finite ele-ment method. Because of the compatibility of Natural reduction with the original variationalformulation, this coupling is natural and direct. It is just a distinctive advantage of the methodpresented.