CONVERGENCE OF A FINITE ELEMENT-FINITE VO LUME SCHEME FOR COUPLED ELLIPTIC PARABOLIC EQUATIONS

Convergence of a finite element-finite volume scheme for coupled ellip tic-parabolic equations. We study here a discretization scheme for the following coupled system of equations: [GRAPHICS] defined over a boun ded open set OMEGA of R2 or R3. A triangular mesh is used for the spac e discretization of both equations, in the case of two space dimension s (a tetrahedral mesh is used in the 3D case). The time discretization of the first equation is performed with the explicit Euler scheme, wh ile its space discretization uses a weighted finite volume method. A f inite element method is used for the elliptic equation. The numerical scheme thus defined converges, under a usual stability condition, in t he sense that a family of approximate solutions converges, when the me sh size tends to 0, towards a solution of the original coupled system. This result is proven via an estimate on the total variation of the a pproximate solutions. Note that it also yields the existence of a solu tion to this system of equations.