A finite element method for time fractional partial differential equations

被引：0
作者：
Neville J. Ford
Jingyu Xiao
Yubin Yan
机构：
[1] University of Chester,Department of Mathematics
[2] Harbin Institute of Technology,Department of Mathematics
来源：
Fractional Calculus and Applied Analysis | 2011年 / 14卷
关键词：
fractional partial differential equations; finite element method; error estimates; numerical examples; Primary 65M12; Secondary 65M06, 65M60, 65M70, 35S10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we consider the finite element method for time fractional partial differential equations. The existence and uniqueness of the solutions are proved by using the Lax-Milgram Lemma. A time stepping method is introduced based on a quadrature formula approach. The fully discrete scheme is considered by using a finite element method and optimal convergence error estimates are obtained. The numerical examples at the end of the paper show that the experimental results are consistent with our theoretical results.
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页码：454 / 474
页数：20
相关论文
共 65 条
[1]  
Adolfsson K.(2003)Adaptive discretization of integro-differential equation with a weakly singular convolution kernel Comput. Methods Appl. Mech. Engrg. 192 5285-5304
[2]  
Enelund M.(2004)Adaptive discretization of fractional order viscoelasticity using sparse time history Comput. Methods Appl. Mech. Engrg. 193 4567-4590
[3]  
Larsson S.(1996)Subdiffusion and anomalous local viscoelasticity in actin networks Phys. Rev. Lett. 77 4470-138
[4]  
Adolfsson K.(2000)Form continuous time random walks to the fractional Fokker-Planck equation Phys. Rev. E 61 132-250
[5]  
Enelund M.(1996)The Green function of the diffusion of fluids in porous media with memory Rend. Fis. Acc. Lincei (Ser. 9) 7 243-493
[6]  
Larsson S.(1997)Generalized compound quadrature formulae for finite-part integrals IMA J. Numer. Anal. 17 479-6
[7]  
Amblard F.(1997)An algorithm for the numerical solution of differential equations of fractional order Electronic Trans. on Numerical Analysis 5 1-773
[8]  
Maggs A. C.(2005)Algorithms for the fractional calculus: A selection of numerical methods Computer Methods in Appl. Mechanics and Engineering 194 743-346
[9]  
Yurke B.(2001)The numerical solution of fractional differential equations: speed versus accuracy Numer. Algorithms 26 333-576
[10]  
Pargellis A. N.(2006)Variational formulation for the stationary fractional advection dispersion equation Numerical Meth. P.D.E. 22 558-281
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