Displaying similar documents to “Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis”

The G method for heterogeneous anisotropic diffusion on general meshes

Léo Agélas, Daniele A. Di Pietro, Jérôme Droniou (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In the present work we introduce a new family of cell-centered Finite Volume schemes for anisotropic and heterogeneous diffusion operators inspired by the MPFA L method. A very general framework for the convergence study of finite volume methods is provided and then used to establish the convergence of the new method. Fairly general meshes are covered and a computable sufficient criterion for coercivity is provided. In order to guarantee consistency in the presence of heterogeneous ...

Diffusion with dissolution and precipitation in a porous medium: Mathematical analysis and numerical approximation of a simplified model

Nicolas Bouillard, Robert Eymard, Raphaele Herbin, Philippe Montarnal (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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Modeling the kinetics of a precipitation dissolution reaction occurring in a porous medium where diffusion also takes place leads to a system of two parabolic equations and one ordinary differential equation coupled with a stiff reaction term. This system is discretized by a finite volume scheme which is suitable for the approximation of the discontinuous reaction term of unknown sign. Discrete solutions are shown to exist and converge towards a weak solution of the continuous...

Mathematical study of a petroleum-engineering scheme

Robert Eymard, Raphaèle Herbin, Anthony Michel (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Models of two phase flows in porous media, used in petroleum engineering, lead to a system of two coupled equations with elliptic and parabolic degenerate terms, and two unknowns, the saturation and the pressure. For the purpose of their approximation, a coupled scheme, consisting in a finite volume method together with a phase-by-phase upstream weighting scheme, is used in the industrial setting. This paper presents a mathematical analysis of this coupled scheme, first showing that...

Discretization methods with analytical characteristic methods for advection-diffusion-reaction equations and 2d applications

Jürgen Geiser (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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Our studies are motivated by a desire to model long-time simulations of possible scenarios for a waste disposal. Numerical methods are developed for solving the arising systems of convection-diffusion-dispersion-reaction equations, and the received results of several discretization methods are presented. We concentrate on linear reaction systems, which can be solved analytically. In the numerical methods, we use large time-steps to achieve long simulation times of about 10 000 years. We...

Some abstract error estimates of a finite volume scheme for a nonstationary heat equation on general nonconforming multidimensional spatial meshes

Abdallah Bradji, Jürgen Fuhrmann (2013)

Applications of Mathematics

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A general class of nonconforming meshes has been recently studied for stationary anisotropic heterogeneous diffusion problems, see Eymard et al. (IMA J. Numer. Anal. 30 (2010), 1009–1043). Thanks to the basic ideas developed in the stated reference for stationary problems, we derive a new discretization scheme in order to approximate the nonstationary heat problem. The unknowns of this scheme are the values at the centre of the control volumes, at some internal interfaces, and at the...

An IMEX scheme for reaction-diffusion equations: application for a PEM fuel cell model

István Faragó, Ferenc Izsák, Tamás Szabó, Ákos Kriston (2013)

Open Mathematics

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An implicit-explicit (IMEX) method is developed for the numerical solution of reaction-diffusion equations with pure Neumann boundary conditions. The corresponding method of lines scheme with finite differences is analyzed: explicit conditions are given for its convergence in the ‖·‖∞ norm. The results are applied to a model for determining the overpotential in a proton exchange membrane (PEM) fuel cell.