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On Schwarz alternating methods for the incompressible Navier–Stokes equations. (English) Zbl 1008.76077
Author’s summary: The Schwarz alternating method can be used to solve linear elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which result from solving a sequence of elliptic boundary value problems in each of the subdomains. This paper considers four Schwarz alternating methods for \(N\)-dimensional steady viscous incompressible Navier-Stokes equations, \(N\leq 4\). It is shown that the Schwarz sequences converge to the true solution provided that the Reynolds number is sufficiently small.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
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