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Zbl 0857.65116
Baranger, Jacques; Maitre, Jean-François; Oudin, Fabienne
Connection between finite volume and mixed finite element methods. (English)
[J] RAIRO, Modélisation Math. Anal. Numér. 30, No.4, 445-465 (1996). ISSN 0764-583X

Authors' abstract: For the model problem with Laplacian operator, we show how to produce cell-centered finite volume schemes, starting from the mixed dual formulation discretized with the Raviart-Thomas element of lowest order.\par The method is based on the use of an appropriate integration formula (mass lumping) allowing an explicit elimination of the vector variables. The analysis of the finite volume scheme (well-posedness and error bounds) is directly deduced from classical results of mixed finite element theory, which is the main interest of the method.\par We emphasize existence and properties of the diagonalizing integration formulas, specially in the case of $N$-dimensional simplicial elements.
[P.Burda (Praha)]

MSC 2000:: *65N30 Finite numerical methods (BVP of PDE)
65N15 Error bounds (BVP of PDE)
35J25 Second order elliptic equations, boundary value problems

Keywords: mixed finite element method; finite volume method; Laplace equation; Raviart-Thomas element; error bounds

Cited in: Zbl 1098.65115

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