On the convergence rate of finite difference methods for degenerate convection-diffusion equations in several space dimensions (Q2806043)

This work aims to derive the error estimates for a class of finite difference methods of nonlinear, possibly strongly degenerate, convection-diffusion problems; particularly this is aimed at entropy solutions to convection-diffusion equations. The monotone methods make use of an upwind discretisation of the convection term and a centred discretisation for the parabolic term. It is shown that the local \(L^1\)-error is \(O(\Delta x ^{2/(19+d)})\), where \(d\) is the spatial dimension. The proof provided makes use of specific kinetic formulations of the difference method and the convection-diffusion equation.