Coupling of Viscous and Inviscid Stokes Equations via a Domain Decomposition Method for Finite Elements

摘要

The generalized Stokes problem, as well as its inviscid counterpart obtained by taking the viscosity coefficient nu = 0, are faced through a domain decomposition approach. Then the reduced problem, arising from the coupling of the inviscid counterpart within a subregion Omega(sub 1) of the physical domain Omega and the Stokes problem within Omega(sub 2) = Omega/Omega(sub 1) is considered. Correct transmission conditions across the interface gamma between Omega(sub 1) and Omega(sub 2) are devised, and an iterative procedure involving the successive resolution of the two subproblems is proposed. For all problems here considered, appropriate finite element approximations are proposed and analyzed. In particular, it is proven 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.