The aim of this paper is the numerical treatment of a boundary value
problem for the system of Stokes' equations. For this we extend the method
of approximate approximations to boundary value problems. This method
was introduced by V. Maz'ya in 1991 and has been used until now for the
approximation of smooth functions defined on the whole space and for the
approximation of volume potentials.
In the present paper we develop an approximation procedure for the solution
of the interior Dirichlet problem for the system of Stokes' equations in
two dimensions. The procedure is based on potential theoretical considerations
in connection with a boundary integral equations method and consists
of three approximation steps as follows.
In a first step the unknown source density in the potential representation of
the solution is replaced by approximate approximations. In a second step the
decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in a third step Nyström's method leads to a linear algebraic system for the approximate source density. For every
step a convergence analysis is established and corresponding error estimates