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arXiv · 1411.4538

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

Kenneth Hvistendahl Karlsen·Nils Henrik Risebro·Erlend Briseid Storrøsten
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Abstract

We analyze upwind difference methods for strongly degenerate convection-diffusion equations in several spatial dimensions. We prove that the local $L^1$-error between the exact and numerical solutions is $\mathcal{O}(\Delta x^{2/(19+d)})$, where $d$ is the spatial dimension and $\Delta x$ 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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Kenneth Hvistendahl Karlsen, Nils Henrik Risebro, Erlend Briseid Storrøsten. 2014-11-17. On the convergence rate of finite difference methods for degenerate convection-diffusion equations in several space dimensions. https://arxiv.org/abs/1411.4538

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