An enriched finite element method to fractional advection-diffusion   equation

doi:10.1007/s00466-017-1400-9

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	An enriched finite element method to fractional advection-diffusion equation
	Luan, Shengzhi ; Lian, Yanping ; Ying, Yuping ; Tang, Shaoqiang ; Wagner, Gregory J. ; Liu, Wing Kam
刊名	COMPUTATIONAL MECHANICS
	2017
关键词	Anomalous diffusion Fractional advection-diffusion equation Fractional calculus Petrov-Galerkin formulation
DOI	10.1007/s00466-017-1400-9
英文摘要	In this paper, an enriched finite element method with fractional basis for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.; ARO [W911NF-15-1-0569]; China Scholarship Council; National Nature Science Foundation of China [11272009, 11521202]; SCI(E); ARTICLE; 2; 181-201; 60
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/471750]
专题	工学院
推荐引用方式 GB/T 7714	Luan, Shengzhi,Lian, Yanping,Ying, Yuping,et al. An enriched finite element method to fractional advection-diffusion equation[J]. COMPUTATIONAL MECHANICS,2017.
APA	Luan, Shengzhi,Lian, Yanping,Ying, Yuping,Tang, Shaoqiang,Wagner, Gregory J.,&Liu, Wing Kam.(2017).An enriched finite element method to fractional advection-diffusion equation.COMPUTATIONAL MECHANICS.
MLA	Luan, Shengzhi,et al."An enriched finite element method to fractional advection-diffusion equation".COMPUTATIONAL MECHANICS (2017).