A numerical algorithm for the Stokes problem based on an integral equation for the pressure via conformal mappings

Summary In this paper we present an algorithm for solving numerically the Stokes problem in the plane. The known algorithms are all based on certain discretization schemes for the analytic equations. In contrast to this recent work our algorithm uses an explicit analytic solution of a certain approximating problem, which can easily be solved numerically up to machine accuracy. On the one hand this analytic formula is based on a complex representation of all solutions of the Stokes differential equations, and on the other hand it is based on the conformal mapping of the given domain on the unit disc. Therefore, a central prerequisite of our corresponding program is a program for computing this conformal mapping.