论文信息 - High-order finite element methods for time-fractional partial differential equations

High-order finite element methods for time-fractional partial differential equations

The aim of this paper is to develop high-order methods for solving time-fractional partial differential equations. The proposed high-order method is based on high-order finite element method for space and finite difference method for time. Optimal convergence rate O((@Dt)^2^-^@a+N^-^r) is proved for the (r-1)th-order finite element method (r>=2).

Jingtang Ma | Yingjun Jiang | Jingtang Ma | Yingjun Jiang | Y. Jiang

[1] Fawang Liu,et al. New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation , 2008, SIAM J. Numer. Anal..

[2] Guy Jumarie,et al. A Fokker-Planck equation of fractional order with respect to time , 1992 .

[3] Kaili Xiang,et al. Numerical simulation of blowup in nonlocal reaction-diffusion equations using a moving mesh method , 2009 .

[4] R. Gorenflo,et al. Time Fractional Diffusion: A Discrete Random Walk Approach , 2002 .

[5] N. Ford,et al. Numerical Solution of the Bagley-Torvik Equation , 2002, BIT Numerical Mathematics.

[6] W. Schneider,et al. Fractional diffusion and wave equations , 1989 .

[7] Chuanju Xu,et al. Finite difference/spectral approximations for the time-fractional diffusion equation , 2007, J. Comput. Phys..

[8] I. Turner,et al. Analysis of a discrete non-Markovian random walk approximation for the time fractional diffusion equation , 2005 .

[9] Fawang Liu,et al. Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term , 2009, J. Comput. Appl. Math..

[10] W. Wyss. The fractional diffusion equation , 1986 .

[11] Shyam L. Kalla,et al. Numerical treatment of fractional heat equations , 2008 .

[12] I. Turner,et al. Time fractional advection-dispersion equation , 2003 .

[13] I. Podlubny. Fractional differential equations , 1998 .