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Application of mixed finite element theory to the study of a class of finite difference-volume schemes for elliptic problems. (Application de la théorie des éléments finis mixtes à l’étude d’une classe de schémas aux volumes différences finis pour les problèmes elliptiques.) (French. English summary) Zbl 0804.65102

Summary: We consider the dual mixed formulation of the Dirichlet problem for the Laplace equations. We show that an appropriate numerical integration allows to eliminate gradient variable. In this fashion we explicitly get a scheme in which the only unknowns are the initial ones and which can be understood as a finite volume one. Mixed finite element techniques can be used to obtain error estimations for some finite volume schemes.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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