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

2016 ◽  
Vol 309 ◽  
pp. 388-410 ◽  
Author(s):  
Yanping Lian ◽  
Yuping Ying ◽  
Shaoqiang Tang ◽  
Stephen Lin ◽  
Gregory J. Wagner ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Element Method

An enriched finite element method to fractional advection–diffusion equation

2017 ◽  
Vol 60 (2) ◽  
pp. 181-201 ◽  
Author(s):  
Shengzhi Luan ◽  
Yanping Lian ◽  
Yuping Ying ◽  
Shaoqiang Tang ◽  
Gregory J. Wagner ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Enriched Finite Element Method ◽  
Enriched Finite Element ◽  
Element Method

scholarly journals A Petrov-Galerkin Finite Element Method for Solving the Time-fractional Diffusion Equation with Interface

2018 ◽  
Vol 10 (4) ◽  
pp. 136
Author(s):  
Liwei Shi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Discontinuous Coefficients ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Time Fractional Diffusion Equation ◽  
Element Method

Time-fractional partial differential equation is widely applied in a variety of disciplines, its numerical solution has attracted much attention from researchers in recent years. Time-fractional differential equations with interfaces is a more challenging problem because the governing equation has discontinuous coefficients at interfaces and sometimes singular source term exists. In this paper, we propose a Petrov-Galerkin finite element method for solving the two-dimensional time-fractional diffusion equation with interfaces. In this method, a finite difference scheme is employed in time and a Petrov-Galerkin finite element method is employed in space. Extensive numerical experiments show that for a fractional diffusion equation of order $\alpha$ with interfaces, our method gets to $(2-\alpha)$-order accurate in the $L^2$ and $L^{\infty}$ norm.

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