| Issue |
ESAIM: M2AN
Volume 47, Number 6, November-December 2013
|
|
|---|---|---|
| Page(s) | 1765 - 1781 | |
| DOI | https://doi.org/10.1051/m2an/2013087 | |
| Published online | 11 October 2013 | |
Conservation schemes for convection-diffusion equations with Robin boundary conditions∗,∗∗
Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.
stephane.flotron@epfl.ch; jacques.rappaz@epfl.ch
Received:
6
March
2012
Revised:
23
April
2013
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.
Mathematics Subject Classification: 65M60 / 35K20 / 80A20
Key words: Finite Elements / numerical conservation schemes / Robin boundary condition / convection-diffusion equations
© EDP Sciences, SMAI 2013
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