Error estimates for two-level penalty finite volume method for the stationary Navier-Stokes equations

2013 ◽  
Vol 36 (14) ◽  
pp. 1918-1928 ◽  
Author(s):  
Pengzhan Huang ◽  
Xinlong Feng
Keyword(s):  
Finite Volume Method ◽  
Error Estimates ◽  
Finite Volume ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
Stationary Navier Stokes Equations

scholarly journals A Stabilized Low Order Finite-Volume Method for the Three-Dimensional Stationary Navier-Stokes Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Jian Li ◽  
Xin Zhao ◽  
Jianhua Wu ◽  
Jianhong Yang
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Uniqueness Condition ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
Stationary Navier Stokes Equations ◽  
Superconvergence Results

This paper proposes and analyzes a stabilized finite-volume method (FVM) for the three-dimensional stationary Navier-Stokes equations approximated by the lowest order finite element pairs. The method studies the new stabilized FVM with the relationship between the stabilized FEM (FEM) and the stabilized FVM under the assumption of the uniqueness condition. The results have three prominent features in this paper. Firstly, the error analysis shows that the stabilized FVM provides an approximate solution with the optimal convergence rate of the same order as the usual stabilized FEM solution solving the stationary Navier-Stokes equations. Secondly, superconvergence results on the solutions of the stabilized FEM and stabilized FVM are derived on theH1-norm and theL2-norm for the velocity and pressure. Thirdly, residual technique is applied to obtain theL2-norm error for the velocity without additional regular assumption on the exact solution.

scholarly journals The Optimal L2 Error Estimate of Stabilized Finite Volume Method for the Stationary Navier-Stokes Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Guoliang He ◽  
Jian Su ◽  
Wenqiang Dai
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stabilized Finite Element ◽  
L2 Error Estimate ◽  
Volume Method ◽  
Stationary Navier Stokes Equations

A finite volume method based on stabilized finite element for the two-dimensional stationary Navier-Stokes equations is analyzed. For the P1–P0 element, we obtain the optimal L2 error estimates of the finite volume solution uh and ph. We also provide some numerical examples to confirm the efficiency of the FVM. Furthermore, the effect of initial value for iterative method is analyzed carefully.

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