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Finite volume box schemes and mixed methods. (English) Zbl 0966.65082
This paper deals with the numerical analysis on the Poisson problem of two mixed Petrov-Galerkin finite volume (FV) schemes for equations in divergence form \(\text{div }\varphi(u,\nabla u)= f\). The author introduces the mixed formulation of which the “FVbox” scheme is an approximation. This formulation generates also a second scheme (called “dual FVbox”) which is a cell-centered finite volume scheme for the couple of unknowns \((u,\nabla u)\). The two test spaces are the functions constant per cell both for the conservative and for the flux equations. Also an optimal second-order error estimate for the box scheme is presented.

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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