A convergence result for a parallel algorithm for solving the Navier-Stokes equations

This work is concerned with the convergence/stability analysis of a parallel algorithm which is used to solve the incompressible Navier-Stokes problem. This relies on a splitting of the main differential operator, thanks to which the most important difficulties (nonlinearity and incompressibility) can be considered independently. Thus, one is led to the formulation of subproblems of two kinds which can be solved simultaneously by two different processors. We prove conditional stability and convergence; this can serve to justify the accuracy of previous numerical results.