A priori-estimates on the unknownsare obtained, and along with a topological degree argument they lead to theexistence of a solution of the discrete scheme at each time step . We conclude the proof of the convergence of the scheme toward the continuous problem as mesh size and time step tend toward zero with the limit of the sequence ofdiscrete solutions being a solution to the weak formulation of the problem . The problem iscompleted with homogeneous Dirichlet boundary conditions and is discretizedaccording to a non-uniform Cartesian grid .

Author(s) : Léa Batteux, Thierry Gallouët, Raphaele Herbin, Jean-Claude Latché, Pascal Poullet

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Keywords : problem - time - step - uniform - convergence -

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