A non-conforming finite volume element method of weighted upstream type for the two-dimensional stationary Navier–Stokes system

2008 ◽  
Vol 58 (5) ◽  
pp. 615-634 ◽  
Author(s):  
K. Djadel ◽  
S. Nicaise
Keyword(s):  
Finite Volume ◽  
Stokes System ◽  
Volume Element ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Finite Volume Element Method ◽  
Finite Volume Element ◽  
Element Method

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.

Analysis of a new stabilized finite volume element method based on multiscale enrichment for the Navier-Stokes problem

2016 ◽  
Vol 26 (8) ◽  
pp. 2462-2485 ◽  
Author(s):  
Juan Wen ◽  
Yinnian He ◽  
Xin Zhao
Keyword(s):  
Finite Volume ◽  
Stokes Problem ◽  
Volume Element ◽  
New Method ◽  
Navier Stokes ◽  
Optimal Order ◽  
Finite Volume Element Method ◽  
Content Type ◽  
Finite Volume Element ◽  
Element Method

Purpose The purpose of this paper is to propose a new stabilized finite volume element method for the Navier-Stokes problem. Design/methodology/approach This new method is based on the multiscale enrichment and uses the lowest equal order finite element pairs P1/P1. Findings The stability and convergence of the optimal order in H1-norm for velocity and L2-norm for pressure are obtained. Originality/value Using a dual problem for the Navier-Stokes problem, the convergence of the optimal order in L2-norm for the velocity is obtained. Finally, numerical example confirms the theory analysis and validates the effectiveness of this new method.

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