Two Mixed Finite Element Methods for Time-Fractional Diffusion Equations

2015 ◽  
Vol 70 (1) ◽  
pp. 407-428 ◽  
Author(s):  
Yanmin Zhao ◽  
Pan Chen ◽  
Weiping Bu ◽  
Xiangtao Liu ◽  
Yifa Tang
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Mixed Finite Element ◽  
Fractional Diffusion ◽  
Mixed Finite Element Methods ◽  
Diffusion Equations ◽  
Fractional Diffusion Equations

Finite element methods for fractional diffusion equations

2020 ◽  
Vol 11 (04) ◽  
pp. 2030001
Author(s):  
Yue Zhao ◽  
Chen Shen ◽  
Min Qu ◽  
Weiping Bu ◽  
Yifa Tang
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Regularity Theory ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Fractional Diffusion Equations ◽  
The Past ◽  
Time Space ◽  
Engineering Physics ◽  
Substantial Interest

Due to the successful applications in engineering, physics, biology, finance, etc., there has been substantial interest in fractional diffusion equations over the past few decades, and literatures on developing and analyzing efficient and accurate numerical methods for reliably simulating such equations are vast and fast growing. This paper gives a concise overview on finite element methods for these equations, which are divided into time fractional, space fractional and time-space fractional diffusion equations. Besides, we also involve some relevant topics on the regularity theory, the well-posedness, and the fast algorithm.

Moving Finite Element Methods for a System of Semi-Linear Fractional Diffusion Equations

2016 ◽  
Vol 8 (6) ◽  
pp. 911-931 ◽  
Author(s):  
Jingtang Ma ◽  
Zhiqiang Zhou
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Convergence Rates ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Predator Prey ◽  
Fractional Diffusion Equations ◽  
Predator Prey Models ◽  
Derivatives Of ◽  
Moving Finite Element

AbstractThis paper studies a system of semi-linear fractional diffusion equations which arise in competitive predator-prey models by replacing the second-order derivatives in the spatial variables with fractional derivatives of order less than two. Moving finite element methods are proposed to solve the system of fractional diffusion equations and the convergence rates of the methods are proved. Numerical examples are carried out to confirm the theoretical findings. Some applications in anomalous diffusive Lotka-Volterra and Michaelis-Menten-Holling predator-prey models are studied.

Sign in / Sign up

Export Citation Format

Share Document