On the convergence rate of finite difference methods for degenerate   convection-diffusion equations in several space dimensions
  We analyze upwind difference methods for strongly degenerate convection-diffusion equations in several spatial dimensions. We prove that the local $L^1$-error between the exact and numerical solutions is $\mathcal{O}(\Delta x^{2/(19+d)})$, where $d$ is the spatial dimension and $\Delta x$ is the grid size. The error estimate is robust with respect to vanishing diffusion effects. The proof makes effective use of specific kinetic formulations of the difference method and the convection-diffusion equation. 
Kenneth Hvistendahl Karlsen, Nils Henrik Risebro, Erlend Briseid   Storr{\o}sten
math.AP