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