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Coupling finite difference methods and integral formulas for elliptic problems arising in fluid mechanics
Author(s) -
Albuquerque C.,
Cottet G.H.
Publication year - 2004
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.10089
Subject(s) - mathematics , domain decomposition methods , partial differential equation , numerical analysis , convergence (economics) , finite difference , schwarz alternating method , finite difference method , boundary value problem , domain (mathematical analysis) , continuation , mathematical analysis , finite element method , computer science , programming language , physics , economics , thermodynamics , economic growth
This article is devoted to the numerical analysis of two classes of iterative methods that combine integral formulas with finite‐difference Poisson solvers for the solution of elliptic problems. The first method is in the spirit of the Schwarz domain decomposition method for exterior domains. The second one is motivated by potential calculations in free boundary problems and can be viewed as a numerical analytic continuation algorithm. Numerical tests are presented that confirm the convergence properties predicted by numerical analysis. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 199–229, 2004