scholarly journals Very high-order accurate finite volume scheme on curved boundaries for the two-dimensional steady-state convection–diffusion equation with Dirichlet condition

2018 ◽  
Vol 54 ◽  
pp. 752-767 ◽  
Author(s):  
Ricardo Costa ◽  
Stéphane Clain ◽  
Raphaël Loubère ◽  
Gaspar J. Machado
Keyword(s):  
Steady State ◽  
Diffusion Equation ◽  
Finite Volume ◽  
Dirichlet Condition ◽  
Finite Volume Scheme ◽  
Two Dimensional ◽  
Curved Boundaries ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Very High

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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