On Schwarz alternating methods for the incompressible Navier-Stokes equations

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 ea...

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Bibliographic Details
Published in:SIAM journal on scientific computing 2001, Vol.22 (6), p.1974-1986
Main Author: LUI, S. H
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary value problems
Exact sciences and technology
Mathematics
Methods
Navier-Stokes equations
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, boundary value problems
Reynolds number
Sciences and techniques of general use
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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 the 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.
ISSN:1064-8275
1095-7197
DOI:10.1137/S1064827598347411