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Finite Element Methods for the Stokes System in Three-Dimensional Exterior Domains

✍ Scribed by Paul Deuring

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 373 KB
Volume: 20
Category: Article
ISSN: 0170-4214
DOI: 10.1002/(sici)1099-1476(199702)20:3<245::aid-mma856>3.0.co;2-f

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✦ Synopsis

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 ¸-Sobolev spaces. These estimates are analogous to corresponding results which are known for the Poisson equation.

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