6 research outputs found

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

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    We analyze upwind difference methods for strongly degenerate convection-diffusion equations in several spatial dimensions. We prove that the local L1L^1-error between the exact and numerical solutions is O(Δx2/(19+d))\mathcal{O}(\Delta x^{2/(19+d)}), where dd is the spatial dimension and Δx\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
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