Discontinuous Galerkin method for fractional convection-diffusion equations

We propose a discontinuous Galerkin method for convection-subdiffusion equations with a fractional operator of order alpha [1,2] 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 stabilityand optimal order of convergence O(h^(k+1)) for subdiffusion, and an order of convergence of O(h^(k+1/2)) is established for the general fractional convection-diffusion problem. The analysis is confirmed by numerical examples.


Published in:
Siam Journal on Numerical Analysis, 52, 1, 405-423
Year:
2014
Publisher:
Philadelphia, Society for Industrial and Applied Mathematics
ISSN:
0036-1429
Keywords:
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 Record created 2013-11-22, last modified 2018-01-28

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