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High-Order Accurate Runge-Kutta (Local) Discontinuous Galerkin Methods for One- and Two-Dimensional Fractional Diffusion Equations

Published online by Cambridge University Press:  28 May 2015

Xia Ji  and
Huazhong Tang
Xia Ji*
Affiliation:
LSEC, Institute of Computational Mathematics, Chinese Academy of Sciences, P. O. Box 2719, Beijing 100190, China
Huazhong Tang*
Affiliation:
HEDPS, CAPT and LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China
*
Corresponding author.Email address:[email protected]
Corresponding author.Email address:[email protected]
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Abstract

As the generalization of the integer order partial differential equations (PDE), the fractional order PDEs are drawing more and more attention for their applications in fluid flow, finance and other areas. This paper presents high-order accurate Runge-Kutta local discontinuous Galerkin (DG) methods for one- and two-dimensional fractional diffusion equations containing derivatives of fractional order in space. The Caputo derivative is chosen as the representation of spatial derivative, because it may represent the fractional derivative by an integral operator. Some numerical examples show that the convergence orders of the proposed local Pk-DG methods are O(hk+1) both in one and two dimensions, where Pk denotes the space of the real-valued polynomials with degree at most k.

Keywords

35R1165M6065M12Discontinuous Galerkin methodRunge-Kutta time discretizationfractional derivativeCaputo derivativediffusion equation
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 5 , Issue 3 , August 2012 , pp. 333 - 358
Copyright
Copyright © Global Science Press Limited 2012

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