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

Abstract

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 $L_{\mathrm{loc}}^1$ 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.

8 Pages. HYP-2012 Proceedings