Error Estimate and the Geometric Corrector for the Upwind Finite Volume Method Applied to the Linear Advection Equation

2005 ◽  
Vol 43 (2) ◽  
pp. 578-603 ◽  
Author(s):  
Daniel Bouche ◽  
Jean-Michel Ghidaglia ◽  
Frédéric Pascal
Keyword(s):  
Error Estimate ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Advection Equation ◽  
Linear Advection Equation ◽  
Volume Method

scholarly journals A Discontinuous Finite Volume Method for the Darcy-Stokes Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Zhe Yin ◽  
Ziwen Jiang ◽  
Qiang Xu
Keyword(s):  
Error Estimate ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Stokes Equations ◽  
Optimal Error Estimate ◽  
Optimal Error ◽  
Numerical Examples ◽  
First Order ◽  
Theoretical Predictions ◽  
Volume Method

This paper proposes a discontinuous finite volume method for the Darcy-Stokes equations. An optimal error estimate for the approximation of velocity is obtained in a mesh-dependent norm. First-orderL2-error estimates are derived for the approximations of both velocity and pressure. Some numerical examples verifying the theoretical predictions are presented.

scholarly journals Improved finite volume method for solving 1-D advection equation

2019 ◽  
Vol 1300 ◽  
pp. 012075
Author(s):  
Siyuan Zhao ◽  
Junjie Zhou ◽  
Chongbo Jing ◽  
Lingquan Li
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Advection Equation ◽  
Volume Method

scholarly journals Convergence Analysis of a Discontinuous Finite Volume Method for the Signorini Problem

2020 ◽  
Vol 12 (4) ◽  
pp. 49
Author(s):  
Yuping Zeng ◽  
Fen Liang
Keyword(s):  
Exact Solution ◽  
Error Estimate ◽  
Convergence Analysis ◽  
Finite Volume Method ◽  
Finite Volume ◽  
A Priori ◽  
Energy Norm ◽  
Signorini Problem ◽  
A Priori Error Estimate ◽  
Volume Method

We introduce and analyze a discontinuous finite volume method for the Signorini problem. Under suitable regularity assumptions on the exact solution, we derive an optimal a priori error estimate in the energy norm.

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