scholarly journals A finite element approximation for a class of Caputo time-fractional diffusion equations

2019 ◽  
Vol 78 (5) ◽  
pp. 1334-1344 ◽  
Author(s):  
Moulay Rchid Sidi Ammi ◽  
Ismail Jamiai ◽  
Delfim F.M. Torres
Keyword(s):  
Finite Element ◽  
Finite Element Approximation ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Element Approximation ◽  
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.

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