Year: 2012
Author: R. A. Klausen, A. F. Stephansen
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 3 : pp. 584–606
Abstract
The analysis of the Multi Point Flux Approximation (MPFA) method has so far relied on the possibility of seeing it as a mixed finite element method for which the convergence is then established. This type of analysis has been successfully applied to triangles and quadrilaterals, also in the case of rough meshes. The MPFA method has however much in common with another well known conservative method: the mimetic finite difference method. We propose to formulate the MPFA O-method in a mimetic finite difference framework, in order to extend the proof of convergence to polyhedral meshes. The formulation is useful to see the close relationship between the two different methods and to see how the differences lead to different strengths. We pay special attention to the assumption needed for proving convergence by examining various cases in the section dedicated to numerical tests.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2012-IJNAM-648
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 3 : pp. 584–606
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Polygonal and polyhedral mesh convergence multi-point flux approximation MPFA O-method mimetic finite difference.