An error estimate for viscous approximate solutions to degenerate anisotropic convection-diffusion equations

We consider a viscous approximation for a nonlinear degenerate convection-diffusion equations in two space dimensions, and prove an $L^1$ error estimate. Precisely, we show that the $L^1_{\mathrm{loc}}$ difference between the approximate solution and the unique entropy solution converges at a rate $\mathcal{O}(\eps^{1/2})$, where $\eps$ is the viscous parameter.