title: Convergence of a finite volume scheme for nonlinear degenerate parabolic equations
abstract: One approximates the entropy weak solution u of a nonlinear parabolic degenerate equation u/sub t/+div(qf(u))- Delta phi (u)=0 by a piecewise constant function u/sub D/ using a discretization D in space and time and a finite volume scheme. The convergence of u/sub D/ to u is shown as the size of the space and time steps tend to zero. In a first step, estimates on u/sub D/ are used to prove the convergence, up to a subsequence, of u/sub D/ to a measure valued entropy solution (called here an entropy process solution). A result of uniqueness of the entropy process solution is proved, yielding the strong convergence of u/sub D/ to u. Some numerical results on a model equation are shown
keyphrases: finite volume scheme nonlinear degenerate parabolic equations entropy weak solution piecewise constant function strong convergence numerical results model equation