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Analysis of a Chimera method. (English. Abridged French version) Zbl 0988.65117

Summary: Chimera is a variant of Schwarz’ algorithm which is used in computational fluid dynamics to avoid meshing complicated objects. In a previous publication F. Hecht, J.-L. Lions and O. Pironneau [Sequeira, Adélia (ed.) et al., Applied nonlinear analysis. In honor of the 70th birthday of Professor Jindřich Neǎs. New York, NY: Kluwer Academic/Plenum Publishers. 185-198 (1999; Zbl 0954.65010)] proposed an implementation for which convergence could be shown except that ellipticity was not proved for the discretized bilinear form with quadrature rules. Here we prove that the bilinear form of the discrete problem is strongly elliptic without compatibility condition for the mesh of the subdomains in their region of intersection.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs

Citations:

Zbl 0954.65010
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