FINITE ELEMENT METHODS FOR THE STOKES SYSTEM IN THREE-DIMENSIONAL EXTERIOR DOMAINS

摘要

The article treats the question of how to numerically solve the Dirichlet problem for the Stokes system in the exterior of a three-dimensional bounded Lipschitz domain. In a first step, the solution of this problem is approximated by functions solving the Stokes system in a truncated domain and satisfying a suitable artificial boundary condition on the outer boundary of this truncated domain. In a second step, this new problem is approximately solved in finite element spaces related to a graded mesh as introduced by Goldstein [Math. Comp., 36, 387-404(1981)]. The difference between this finite element approximation and the exact solution of the exterior Stokes problem is estimated in the norm of suitable unweighted L(2)-Sobolev spaces. These estimates are analogous to corresponding results which are known for the Poisson equation. [References: 39]