An error estimate for the finite difference approximation to degenerate convection–diffusion equations

We consider semi-discrete first-order finite difference schemes for a nonlinear degenerate convection–diffusion equations in one space dimension, and prove an L 1 error estimate. Precisely, we show that the difference between the approximate solution and the unique entropy solution converges at a rate , where is the spatial mesh size. If the diffusion is linear, we get the convergence rate , the point being that the is independent of the size of the diffusion.