A Petrov-Galerkin finite element method for the fractional   advection-diffusion equation

doi:10.1016/j.cma.2016.06.013

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	A Petrov-Galerkin finite element method for the fractional advection-diffusion equation
	Lian, Yanping ; Ying, Yuping ; Tang, Shaoqiang ; Lin, Stephen ; Wagner, Gregory J. ; Liu, Wing Kam
刊名	COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
	2016
关键词	Non-local diffusion Fractional advection-diffusion equation Fractional calculus Petrov-Galerkin formulation COMPUTATIONAL FLUID-DYNAMICS FORMULATION DISPERSION SUPG
DOI	10.1016/j.cma.2016.06.013
英文摘要	This paper presents an in-depth numerical analysis of spatial fractional advection diffusion equations (FADE) utilizing the finite element method (FEM). A traditional Galerkin finite element formulation of the pure fractional diffusion equation without advection may yield numerical oscillations in the solution depending on the fractional derivative order. These oscillations are similar to those that may arise in the integer-order advection-diffusion equation when using the Galerkin FEM. In a Galerkin formulation of a FADE, these oscillations are further compounded by the presence of the advection term, which we show can be characterized by a fractional element Peclet number that takes into account the fractional order of the diffusion term. To address this oscillatory behavior, a Petrov-Galerkin method is formulated using a fractional stabilization parameter to eliminate the oscillatory behavior arising from both the fractional diffusion and advection terms. A compact formula for an optimal fractional stabilization parameter is developed through a minimization of the residual of the nodal solution. Steady state and transient one-dimensional cases of the pure fractional diffusion and fractional advection-diffusion equations are implemented to demonstrate the effectiveness and accuracy of the proposed formulation. (C) 2016 Elsevier B.V. AU rights reserved.; ARO grant [W911NF-15-1-0569]; Office of China Postdoctoral Council under the International Postdoctoral Exchange Fellowship; China Scholarship Council; National Natural Science Foundation of China [11272009, 11521202]; SCI(E); EI; ARTICLE; w-liu@northwestern.edu; 388-410; 309
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/494360]
专题	工学院
推荐引用方式 GB/T 7714	Lian, Yanping,Ying, Yuping,Tang, Shaoqiang,et al. A Petrov-Galerkin finite element method for the fractional advection-diffusion equation[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2016.
APA	Lian, Yanping,Ying, Yuping,Tang, Shaoqiang,Lin, Stephen,Wagner, Gregory J.,&Liu, Wing Kam.(2016).A Petrov-Galerkin finite element method for the fractional advection-diffusion equation.COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING.
MLA	Lian, Yanping,et al."A Petrov-Galerkin finite element method for the fractional advection-diffusion equation".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2016).