A Finite Volume Scheme for Nonlinear Degenerate Parabolic Equations

We propose a second order finite volume scheme for nonlinear degenerate parabolic equations which admit an entropy functional. For some of these models (porous media equation, drift-diffusion system for semiconductors) it has been proved that the transient solution converges to a steady state when time goes to infinity. The present scheme preserves steady states and provides a satisfying long time behavior. Moreover, it remains valid and second order accurate in space even in the degenerate case. After describing the numerical scheme, we present several numerical results which confirm the high order accuracy in various regime degenerate and nondegenerate cases and underline the efficiency to preserve the large time asymptotic.