Coupling of the Finite Volume Method and the Boundary Element Method - Theory, Analysis, and Numerics
Dissertation
Faculties
Fakultät für Mathematik und WirtschaftswissenschaftenAbstract
We develop a discretization scheme for the coupling of the finite volume method and the boundary element method in two dimensions, which describes, for example, the transport of a concentration in a fluid. The discrete system maintains naturally local conservation. In a bounded interior domain we approximate a diffusion convection reaction problem either by the finite volume element method or by the cell-centered finite volume method, whereas in the corresponding exterior domain the Laplace problem is solved by the boundary element method. On the coupling boundary we have appropriate transmission conditions. A weighted upwind scheme guarantees the stability of the method also for convection dominated problems. We show existence and uniqueness of the continuous system and provide an a~priori analysis for the coupling with the finite volume element method. For both coupling systems we derive residual-based a~posteriori estimates, which give upper and lower bounds for the error between the exact solution and the approximate solution. These bounds measure the error in an energy (semi-) norm and are robust in the sense that they do not depend on the variation of the model data. The local contributions of the a~posteriori estimates are used to steer an adaptive
mesh-refining algorithm. Numerical experiments show that our adaptive coupling is an efficient method for the numerical treatment of transmission problems, which exhibit local behavior.
Date created
2010
Subject headings
[LCSH]: Boundary element methods | Numerical analysis[Free subject headings]: A posteriori error estimation | Cell-centered finite volume method | Coupling | Finite volume element method
[DDC subject group]: DDC 510 / Mathematics
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Please use this identifier to cite or link to this item: http://dx.doi.org/10.18725/OPARU-1794
Erath, Christoph (2010): Coupling of the Finite Volume Method and the Boundary Element Method - Theory, Analysis, and Numerics. Open Access Repositorium der Universität Ulm und Technischen Hochschule Ulm. Dissertation. http://dx.doi.org/10.18725/OPARU-1794
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