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Coupling of viscous and inviscid Stokes equations via a domain decomposition method for finite elements. (English) Zbl 0724.76049
Numer. Math. (to appear).
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 situation 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.
Reviewer: A.Quarternoni

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76D07 Stokes and related (Oseen, etc.) flows
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
Full Text: EuDML