6 research outputs found
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 -error between the exact and numerical solutions is
, where is the spatial dimension and
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