Two-grid methods for expanded mixed finite element approximations of semi-linear parabolic integro-differential equations

2018 ◽  
Vol 132 ◽  
pp. 163-181 ◽  
Author(s):  
Tianliang Hou ◽  
Luoping Chen ◽  
Yin Yang
Keyword(s):  
Finite Element ◽  
Differential Equations ◽  
Mixed Finite Element ◽  
Finite Element Approximations ◽  
Expanded Mixed Finite Element

scholarly journals A New Positive Definite Expanded Mixed Finite Element Method for Parabolic Integrodifferential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Yang Liu ◽  
Hong Li ◽  
Jinfeng Wang ◽  
Wei Gao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Positive Definite ◽  
Integrodifferential Equations ◽  
Fully Discrete ◽  
Mixed Scheme ◽  
Expanded Mixed Finite Element ◽  
Element Method

A new positive definite expanded mixed finite element method is proposed for parabolic partial integrodifferential equations. Compared to expanded mixed scheme, the new expanded mixed element system is symmetric positive definite and both the gradient equation and the flux equation are separated from its scalar unknown equation. The existence and uniqueness for semidiscrete scheme are proved and error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are provided to confirm our theoretical analysis.

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