Convergence of finite volume schemes for semilinear convection diffusion equations

The topic of this work is the discretization of semilinear elliptic problem s in two space dimensions by the cell centered finite volume method. Dirich let boundary conditions are considered here. A discrete Poincare inequality is used, and estimates on the approximate solutions are proven. The conver gence of the scheme without any assumption on the regularity of the exact s olution is proven using some compactness results which are shown to hold fo r the approximate solutions. Mathematics Subject Classification (1991): 65N 12.