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An Error Estimate for the Finite Difference Approximation to Degenerate Convection -Diffusion Equations by Karlsen, K. H.; Koley, U.; Risebro, N. H. is a scholarly article available to read on EtoBox.

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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

Author

Karlsen, K. H.; Koley, U.; Risebro, N. H.

Published

2011

Language

EN