COUPLING OF VISCOUS AND INVISCID STOKES EQUATIONS VIA A DOMAIN DECOMPOSITION METHOD FOR FINITE-ELEMENTS

A generalized Stokes problem is addressed in the framework of a domain decomposition method, in which the physical computational domain OMEGA is partitioned into two subdomains OMEGA-1 and OMEGA-2. Three different situations are covered. In the former, the viscous terms are kept in both subdomains. Then we consider the case in which viscosity is dropped out everywhere in OMEGA. Finally, a hybrid situation in which viscosity is dropped out only in OMEGA-1 is addressed. The latter is motivated by physical applications. In all cases, correct transmission conditions across the interface GAMMA between OMEGA-1 and OMEGA-2 are devised, and an iterative procedure involving the successive resolution of two subproblems is proposed. The numerical discretization is based upon appropriate finite elements, and stability and convergence analysis is carried out. We also prove that the iteration-by-subdomain algorithms which are associated with the various domain decomposition approaches converge with a rate independent of the finite element mesh size.