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Conservation schemes for convection-diffusion equations with Robin boundary conditions∗∗∗

Published online by Cambridge University Press:  11 October 2013

Stéphane Flotron  and
Jacques Rappaz
Stéphane Flotron
Affiliation:
Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.. stephane.flotron@epfl.ch; jacques.rappaz@epfl.ch
Jacques Rappaz
Affiliation:
Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.. stephane.flotron@epfl.ch; jacques.rappaz@epfl.ch
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Abstract

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 we give some numerical examples which show the efficiency of the method.

Keywords

Finite Elementsnumerical conservation schemesRobin boundary conditionconvection-diffusion equations
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 6 , November 2013 , pp. 1765 - 1781
Copyright
© EDP Sciences, SMAI 2013

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