L1 Error Estimates for Difference Approximations Of Degenerate   Convection-Diffusion Equations
  We analyze monotone difference schemes for strongly degenerate convection-diffusion equations in one spatial dimension. These nonlinear equations are well-posed within a class of (discontinuous) entropy solutions. We prove that the L1 difference between the approximate solutions and the unique entropy solution is bounded above by a constant times the cube root of the spatial discretization parameter. 
Kenneth H. Karlsen, Nils Henrik Risebro, Erlend B. Storr{\o}sten
math.AP