Domain decomposition methods with applications to fluid dynamics

Abstract

In this presentation, a brief review of domain decomposition methods with emphasis on the applications to solving elliptic problems arising from the Navier-Stokes equations via operator splitting methods is given. The singularly perturbed convection-diffusion equation is chosen as a model problem. We consider both overlapping (multiplicative and additive Schwarz) and nonoverlapping (Neumann-Dirichlet and Neumann-Neumann) domain decomposition methods. Some convergence results for particular cases are presented.