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numerical conservation schemes

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Conservation schemes for convection-diffusion equations withRobin boundary conditions ∗∗∗
Stéphane Flotron, Jacques Rappaz
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 47 / Issue 6 / November 2013

Published online by Cambridge University Press:

11 October 2013, pp. 1765-1781

Print publication:

November 2013
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In this article, we present a numerical scheme based on a finite element method in orderto solve a time-dependent convection-diffusion equation problem and satisfy someconservation properties. In particular, our scheme is able to conserve the total energyfor 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. Weestablish a priori errror estimates for this scheme and we give some numerical exampleswhich show the efficiency of the method.