Solution of the porous media equation by a compact finite difference method.
Sari, Murat (2009)
Mathematical Problems in Engineering
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Sari, Murat (2009)
Mathematical Problems in Engineering
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Jozef Kačur, Roger Van Keer (2003)
Applications of Mathematics
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Numerical approximation schemes are discussed for the solution of contaminant transport with adsorption in dual-well flow. The method is based on time stepping and operator splitting for the transport with adsorption and diffusion. The nonlinear transport is solved by Godunov’s method. The nonlinear diffusion is solved by a finite volume method and by Newton’s type of linearization. The efficiency of the method is discussed.
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...
Kačur, J., Remešíková, M., Malengier, B.
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Dehghan, Mehdi (2005)
Mathematical Problems in Engineering
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Stéphane Flotron, Jacques Rappaz (2013)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In this article, we present a numerical scheme based on a finite element method in order to solve a time-dependent convection-diffusion equation problem and satisfy some conservation properties. In particular, our scheme is able to conserve the total energy for a heat equation or the total mass of a solute in a fluid for a concentration equation, even if the approximation of the velocity field is not completely divergence-free. We establish a priori errror estimates for this scheme and...