scholarly journals The Upwind Finite Volume Element Method for Two-Dimensional Burgers Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Qing Yang
Keyword(s):  
Finite Volume ◽  
Burgers Equation ◽  
Volume Element ◽  
Two Dimensional ◽  
Finite Volume Element Method ◽  
Nonlinear Convection ◽  
Discrete Scheme ◽  
Fully Discrete ◽  
Finite Volume Element ◽  
Element Method

A finite volume element method for approximating the solution to two-dimensional Burgers equation is presented. Upwind technique is applied to handle the nonlinear convection term. We present the semi-discrete scheme and fully discrete scheme, respectively. We show that the schemes are convergent to order one in space inL2-norm. Numerical experiment is presented finally to validate the theoretical analysis.

scholarly journals The finite volume element method for the two-dimensional space-fractional convection–diffusion equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yanan Bi ◽  
Ziwen Jiang
Keyword(s):  
Diffusion Equation ◽  
Finite Volume ◽  
Dimensional Space ◽  
Volume Element ◽  
Two Dimensional ◽  
Finite Volume Element Method ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Finite Volume Element ◽  
Element Method

AbstractWe develop a fully discrete finite volume element scheme of the two-dimensional space-fractional convection–diffusion equation using the finite volume element method to discretize the space-fractional derivative and Crank–Nicholson scheme for time discretization. We also analyze and prove the stability and convergence of the given scheme. Finally, we validate our theoretical analysis by data from three examples.

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