On Discrete Stokes and Navier—Stokes Equations in the Plane

Abstract

Main goal of the paper is to apply the theory of discrete analytic functions to the solution of Dirichlet problems for the Stokes and Navier-Stokes equations, respectively. The Cauchy-Riemann operator will be approximated by certain finite difference operators. Approximations of the classical T -operator as well as for the Bergman projections are constructed in such a way that the algebraical properties of the operators from the complex function theory remain valid. This is used to approximate the solutions to the boundary value problems by adapted finite difference schemes.