On the numerical solution of the one-dimensional convection-diffusion equation.
Dehghan, Mehdi (2005)
Mathematical Problems in Engineering
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Dehghan, Mehdi (2005)
Mathematical Problems in Engineering
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O. Axelsson (1984)
Banach Center Publications
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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...
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.