scholarly journals An expanded mixed finite element method for two-dimensional Sobolev equations

2019 ◽  
Vol 348 ◽  
pp. 342-355 ◽  
Author(s):  
Na Li ◽  
Ping Lin ◽  
Fuzheng Gao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Two Dimensional ◽  
Sobolev Equations ◽  
Expanded Mixed Finite Element ◽  
Element Method

scholarly journals Expanded Mixed Finite Element Method for the Two-Dimensional Sobolev Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Qing-li Zhao ◽  
Zong-cheng Li ◽  
You-zheng Ding
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Optimal Order ◽  
Two Dimensional ◽  
Sobolev Equation ◽  
Order Error ◽  
Expanded Mixed Finite Element ◽  
Element Method

Expanded mixed finite element method is introduced to approximate the two-dimensional Sobolev equation. This formulation expands the standard mixed formulation in the sense that three unknown variables are explicitly treated. Existence and uniqueness of the numerical solution are demonstrated. Optimal order error estimates for both the scalar and two vector functions are established.

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.

scholarly journals The Time DiscontinuousH1-Galerkin Mixed Finite Element Method for Linear Sobolev Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Hong Yu ◽  
Tongjun Sun ◽  
Na Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Approximate Solutions ◽  
Piecewise Polynomial ◽  
Sobolev Equations ◽  
Time Variables ◽  
Norm Error ◽  
Element Method

We combine theH1-Galerkin mixed finite element method with the time discontinuous Galerkin method to approximate linear Sobolev equations. The advantages of these two methods are fully utilized. The approximate schemes are established to get the approximate solutions by a piecewise polynomial of degree at mostq-1with the time variable. The existence and uniqueness of the solutions are proved, and the optimalH1-norm error estimates are derived. We get high accuracy for both the space and time variables.

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