Displaying similar documents to “Conservation schemes for convection-diffusion equations with Robin boundary conditions”

An efficient linear numerical scheme for the Stefan problem, the porous medium equation and nonlinear cross-diffusion systems

Molati, Motlatsi, Murakawa, Hideki

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This paper deals with nonlinear diffusion problems which include the Stefan problem, the porous medium equation and cross-diffusion systems. We provide a linear scheme for these nonlinear diffusion problems. The proposed numerical scheme has many advantages. Namely, the implementation is very easy and the ensuing linear algebraic systems are symmetric, which show low computational cost. Moreover, this scheme has the accuracy comparable to that of the wellstudied nonlinear schemes and...

On discontinuous Galerkin methods for nonlinear convection-diffusion problems and compressible flow

Vít Dolejší, Miloslav Feistauer, Christoph Schwab (2002)

Mathematica Bohemica

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The paper is concerned with the discontinuous Galerkin finite element method for the numerical solution of nonlinear conservation laws and nonlinear convection-diffusion problems with emphasis on applications to the simulation of compressible flows. We discuss two versions of this method: (a) Finite volume discontinuous Galerkin method, which is a generalization of the combined finite volume—finite element method. Its advantage is the use of only one mesh (in contrast to the combined...

The generalized finite volume SUSHI scheme for the discretization of the peaceman model

Mohamed Mandari, Mohamed Rhoudaf, Ouafa Soualhi (2021)

Applications of Mathematics

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We demonstrate some a priori estimates of a scheme using stabilization and hybrid interfaces applying to 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 of invading fluid. The anisotropic diffusion operators in both equations require special care while discretizing by a finite volume method...

Small-stencil 3D schemes for diffusive flows in porous media

Robert Eymard, Cindy Guichard, Raphaèle Herbin (2012)

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

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In this paper, we study some discretization schemes for diffusive flows in heterogeneous anisotropic porous media. We first introduce the notion of gradient scheme, and show that several existing schemes fall into this framework. Then, we construct two new gradient schemes which have the advantage of a small stencil. Numerical results obtained for real reservoir meshes show the efficiency of the new schemes, compared to existing ones.