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On the convergence rate of the Dirichlet-Neumann iteration for coupled poisson problems on unstructured grids

 
: Görtz, M.; Birken, P.

:

Klöfkorn, R.:
Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples : FVCA 9, Bergen, Norway, June 15-19, 2020, online event
Cham: Springer Nature, 2020 (Springer Proceedings in Mathematics & Statistics 323)
ISBN: 978-3-030-43650-6 (Print)
ISBN: 978-3-030-43651-3 (Online)
S.355-363
International Symposium on Finite Volumes for Complex Applications (FVCA) <9, 2020, Online>
Englisch
Konferenzbeitrag
Fraunhofer FCC ()

Abstract
We consider thermal fluid structure interaction with a partitioned approach, where typically, a finite volume and a finite element code would be coupled. As a model problem, we consider two coupled Poisson problems with heat conductivities λ1, λ2 in one dimension on intervals of length l1 and l2. Hereby, we consider linear discretizations on arbitrary meshes, such as finite volumes, finite differences, finite elements. For these, we prove that the convergence rate of the Dirichlet-Neumann iteration is given by λ1l2/λ2l1 and is thus independent of discretization and mesh.

: http://publica.fraunhofer.de/dokumente/N-602934.html