New implementation techniques for the exterior Stokes problem in the plane

We present a method to solve numerically two-dimensional Stokes problems on exterior domains. Our scheme is based on the fully discrete BEM-FEM formulation proposed in [21] whose main advantage is that only elemental quadratures are used to approximate the weakly singular boundary integrals. We show in this article that it is possible to maintain this important property without using curved triangles in the discretization process. This modification makes the method easier to implement and the numerical experiments reveal that it still keeps the optimal order of convergence of the original scheme. We also introduce in this paper a new iterative method to solve the complicated linear systems of equations that arises from this type of BEM-FEM discretizations. (C) 2001 Academic Press.