三维定常流Stokes问题的边界积分方程法

1.解的积分表示及变分公式 考虑如下Stokes方程的Dirichlet问题:设Ω是具有光滑边界Γ的单连通区域,Ω′=R~3-Ω。所求未知量是充满于Ω或Ω′的不可压缩粘性流体的流速u=(u_1,u_2,u_3)和压力p。这里v是运动粘性系数。 已经证明Nedelec-Communication personnelle]:若u_0∈(H~(1/2)(Γ))~3,且满足

A BOUNDARY INTEGRAL EQUATION METHOD FOR THE STATIONARY STOKES PROBLEM IN THREE DIMENSIONS

In this paper, we present a boundary integral expression for the solution of theDirichlet problem of the stationary Stokes equation in R~3 by use of a simple layer po-tential, and its variational formulation. This formulation allows the use of a finiteelement method. We give an analytical formula for the integration with singularity inthe problem. Numerical results of four test problems are shown by tables and figures.