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On the Finite Volume Reformulation of the Mixed Finite Elements Method on Triangles

Abstract : We analyse the finite volume reformulation of the triangular mixed finite element approximation for the porous flow equation, as proposed in [10] [9]. We show that the finite volumes are obtained by aggregation of finite elements (usually one, sometimes two or more), that the matrix of the finite volume equations is regular, but generally not symmetrical, and that the finite volume formulation is algebraically equivalent to the mixed approximation. The finite volume matrix becomes symmetrical in the stationary case, and positive definite when the triangulation satisfies the Delaunay condition.
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https://hal.inria.fr/inria-00072892
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Submitted on : Wednesday, May 24, 2006 - 11:11:33 AM
Last modification on : Thursday, February 3, 2022 - 11:16:30 AM
Long-term archiving on: : Sunday, April 4, 2010 - 9:09:20 PM

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  • HAL Id : inria-00072892, version 1

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Guy Chavent, Anis Younès, Robert Mosé, Philippe Ackerer. On the Finite Volume Reformulation of the Mixed Finite Elements Method on Triangles. [Research Report] RR-3769, INRIA. 1999. ⟨inria-00072892⟩

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