Equivalence between mixed finite element and multi-point finite volume methods |
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Authors: | Martin Vohralík |
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Institution: | 1. Laboratoire de mathématiques, analyse numérique et EDP, université de Paris-Sud, bâtiment 425, 91405 Orsay, France;2. Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 12000 Prague 2, Czech Republic |
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Abstract: | We consider the lowest-order Raviart–Thomas mixed finite element method for elliptic problems on simplicial meshes in two or three space dimensions. This method produces saddle-point type problems for scalar and flux unknowns. We show how to easily eliminate the flux unknowns, which implies an equivalence between this method and a particular multi-point finite volume scheme, without any approximate numerical integration. We describe the stencil of the final matrix and give sufficient conditions for its symmetry and positive definiteness. We present a numerical example illustrating the performance of the proposed method. To cite this article: M. Vohralík, C. R. Acad. Sci. Paris, Ser. I 339 (2004). |
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