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.

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.

Two-Level Stabilized Finite Volume Methods for the Stationary Navier-Stokes Equations

2013 ◽  
Vol 5 (1) ◽  
pp. 19-35 ◽  
Author(s):  
Tong Zhang ◽  
Shunwei Xu
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Mesh Size ◽  
Finite Volume Methods ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fine Mesh ◽  
Volume Method

AbstractIn this work, two-level stabilized finite volume formulations for the 2D steady Navier-Stokes equations are considered. These methods are based on the local Gauss integration technique and the lowest equal-order finite element pair. Moreover, the two-level stabilized finite volume methods involve solving one small Navier-Stokes problem on a coarse mesh with mesh size H, a large general Stokes problem for the Simple and Oseen two-level stabilized finite volume methods on the fine mesh with mesh size or a large general Stokes equations for the Newton two-level stabilized finite volume method on a fine mesh with mesh size . These methods we studied provide an approximate solution with the convergence rate of same order as the standard stabilized finite volume method, which involve solving one large nonlinear problem on a fine mesh with mesh size h. Hence, our methods can save a large amount of computational time.

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