An error estimate for the finite difference approximation to degenerate convection -diffusion equations

Details An error estimate for the finite difference approximation to degenerate convection -diffusion equations An error estimate for the finite difference approximation to degenerate convection -diffusion equations

2011-02-02

arxiv.org/abs/1102.0493v1

Mathematics

Analysis of PDEs

22 pages

Scientific paper

We consider semi-discrete first-order finite difference schemes for a nonlinear degenerate convection-diffusion equations in one space dimension, and prove an L1 error estimate. Precisely, we show that the L1 loc difference between the approximate solution and the unique entropy solution converges at a rate O(\Deltax 1/11), where \Deltax is the spatial mesh size. If the diffusion is linear, we get the convergence rate O(\Deltax 1/2), the point being that the O is independent of the size of the diffusion

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