New Numerical Approach to the Stokes Problem

摘要

In this paper we deal with the numerical approximation, by means of a finite element method, of the Stokes problem. It is well known that this problem has been (and it is) widely studied from a theoretical and numerical point of view. The basic idea developed in this paper is to use the approach due to Kleiser-Schumann, in which a boundary condition for the pressure is implicitly defined by a condition on the velocity. More exactly, taking the divergence of the momentum equation, the incompressibility condition is enforced by a suitable Poisson equation for the pressure and by the condition on the velocity field to be divergence free at the walls. Then a suitable splitting of the unknowns of the problem allows to reduce the stokes problem to a cascade of classical Dirichlet problems and to a boundary integral equation, whose approximation leads to the solution of a linear system with a symmetric, positive, semi-definite matrix.