Stella Krell

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Abstract. “Discrete Duality Finite Volume” schemes (DDFV for short) on general meshes are studied here for Stokes problems with variable viscosity with Dirichlet boundary conditions. The aim of this work is to analyze the well-posedness of the scheme and its convergence properties. The DDFV method requires a staggered scheme, the discrete unknowns, the(More)
This work is intended to provide a convenient tool for the mathematical analysis of a particular kind of finite volume approximation which can be used, for instance, in the context of nonlinear and/or anisotropic diffusion operators in 3D. Following the so-called DDFV (Disctere Duality Finite Volume) approach developed by F. Hermeline and by K. Domelevo and(More)
A discretization of the Schwarz algorithm using Discrete Duality Finite Volume methods (DDFV for short) for such problems was developed in [3]. The DDFV method needs a dual set of unknowns located on both vertices and “centers” of the primal control volumes, which leads to two meshes, the primal and the dual one, and permits the reconstruction of(More)
This paper gives numerical results for a 3D extension of the 2D DDFV scheme. Our scheme is of the same inspiration as the one called CeVe-DDFV ([9]), with a more straightforward dual mesh construction. We sketch the construction in which, starting from a given 3D mesh (which can be non conformal and have arbitrary polygonal faces), one defines a dual mesh(More)
We consider the homogenization of a coupled system of PDEs describing flows in heterogeneous porous media. Due to the coupling, the effective coefficients always depend on the slow variable, even in the simple case when the porosity is periodic. Therefore the most important part of the computational time for the numerical simulation of such flows is(More)
In this paper, we prove the convergence of a discrete duality finite volume scheme for a system of partial differential equations describing miscible displacement in porous media. This system is made of two coupled equations: an anisotropic diffusion equation on the pressure and a convection-diffusion-dispersion equation on the concentration. We first(More)
In this paper, we are interested in the finite volume approximation of a system describing miscible displacement in porous media. This system is made of two coupled equations: an anisotropic diffusion equation on the pressure and a convection-diffusion-dispersion equation on the concentration of invading fluid. The anisotropic diffusion operators in both(More)
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