scholarly journals A Conservative Flux Optimization Finite Element Method for Convection-diffusion Equations

2019 ◽  
Vol 57 (3) ◽  
pp. 1238-1262 ◽  
Author(s):  
Yujie Liu ◽  
Junping Wang ◽  
Qingsong Zou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equations ◽  
Convection Diffusion ◽  
Conservative Flux ◽  
Element Method

A stabilizer free spatial weak Galerkin finite element methods for time-dependent convection-diffusion equations

2021 ◽  
pp. 1-16
Author(s):  
Ahmed Al-Taweel ◽  
Saqib Hussain ◽  
Xiaoshen Wang ◽  
Mohammed Cheichan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rates Of Convergence ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Weak Galerkin ◽  
Simple Formulation ◽  
Spatial Direction ◽  
Convection Diffusion ◽  
Element Method

In this paper, we propose a stabilizer free spatial weak Galerkin (SFSWG) finite element method for solving time-dependent convection diffusion equations based on weak form Eq. (4). SFSWG method in spatial direction and Euler difference operator Eq. (37) in temporal direction are used. The main reason for using the SFSWG method is because of its simple formulation that makes this algorithm more efficient and its implementation easier. The optimal rates of convergence of 𝒪⁢(hk) and 𝒪⁢(hk+1) in a discrete H1 and L2 norms, respectively, are obtained under certain conditions if polynomial spaces (Pk⁢(K),Pk⁢(e),[Pj⁢(K)]2) are used in the SFSWG finite element method. Numerical experiments are performed to verify the effectiveness and accuracy of the SFSWG method.

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