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Coupling boundary integral and finite element methods for the Oseen coupled problem. (English) Zbl 1037.76039

Summary: We represent an Oseen coupled problem and related numerical method for solving the nonstationary Navier-Stokes problem in an unbounded domain. The Oseen coupled problem consists of a coupling between Navier-Stokes problem in an inner region and Oseen problem in an outer region. The related numerical method consists in coupling the boundary integral and finite element method to solve the coupled problem. The variational formulation of the coupled problem and its well-posedness are obtained. We also provide optimal error estimates between the numerical solution of coupled Oseen problem and the exact solution of the Navier-Stokes problem.

MSC:

76M15 Boundary element methods applied to problems in fluid mechanics
76M10 Finite element methods applied to problems in fluid mechanics
76D07 Stokes and related (Oseen, etc.) flows
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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