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arXiv · 1201.6079

On numerical methods and error estimates for degenerate fractional convection-diffusion equations

Simone Cifani·Espen R. Jakobsen
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Abstract

First we introduce and analyze a convergent numerical method for a large class of nonlinear nonlocal possibly degenerate convection diffusion equations. Secondly we develop a new Kuznetsov type theory and obtain general and possibly optimal error estimates for our numerical methods - even when the principal derivatives have any fractional order between 1 and 2! The class of equations we consider includes equations with nonlinear and possibly degenerate fractional or general Levy diffusion. Special cases are conservation laws, fractional conservation laws, certain fractional porous medium equations, and new strongly degenerate equations.

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Simone Cifani, Espen R. Jakobsen. 2012-01-29. On numerical methods and error estimates for degenerate fractional convection-diffusion equations. https://arxiv.org/abs/1201.6079

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