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arXiv · 1304.6047

Discontinuous Galerkin method for fractional convection-diffusion equations

Q. Xu·J. S. Hesthaven
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Abstract

We propose a discontinuous Galerkin method for convection-subdiffusion equations with a fractional operator of order $\alpha (1<\alpha<2)$ defined through the fractional Laplacian. The fractional operator of order $\alpha$ is expressed as a composite of first order derivatives and fractional integrals of order $2-\alpha$, and the fractional convection-diffusion problem is expressed as a system of low order differential/integral equations and a local discontinuous Galerkin method scheme is derived for the equations. We prove stability and optimal order of convergence O($h^{k+1}$) for subdiffusion, and an order of convergence of ${\cal O}(h^{k+1/2})$ is established for the general fractional convection-diffusion problem. The analysis is confirmed by numerical examples.

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Q. Xu, J. S. Hesthaven. 2013-04-22. Discontinuous Galerkin method for fractional convection-diffusion equations. https://arxiv.org/abs/1304.6047

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