GALLOUËT , Thierry

We give here a comparative study of the mathematical analysis of two (classes of) discretisation schemes for the computation of approximate solutions to incompressible two phase flow problem in homogeneous porous media. The first scheme is the well-known finite volume scheme with a two-point flux approximation, classically used in industry. The...

We show in this paper that the gradient schemes (which encompass a large family of discrete schemes) may be used for the approximation of the Stefan problem $\partial_t \bar u - \Delta \zeta (\bar u) = f$. The convergence of the gradient schemes to the continuous solution of the problem is proved thanks to the following steps. First, estimates...