Navier-Stokes方程两层稳定有限元算法分析

摘要

In this paper,two kinds of two-level stabilized finite element methods based on local Gauss integral lechnique for the two- dimensional staionary Navier- Stokes equations approximated by the lowest equal- order P1 - P1 or Q1-Q1 elements.The error analysis shows that the two-level stabilized finite element methods providce an approximate solution with the convergence rate of the same order as the usual stabilized fiuite element solution solving the Navier- Stokes equations on a fine mesh for a related choice of mesh widths H = O( h1/2 ).Therefore,the two-level methods are of practical importance in scientific computation.Finally,the performance of two kinds of two- level stabitized mthods are compared in effiriency and precision aspects hy a series of numerical experiments.The conclusion is that the simple twolevel stabilized methods is best than the other in accuracy and efficiency.And,there is better numerical accuracy for the Oseen algorithm to N- S equations with low viscosity coefficient.%分析了定常Navier-Stokes方程的两种两层稳定有限元算法.它们将局部Gauss积分稳定化技术和两层算法的思想充分结合,采用低次等阶有限元P1-P1或Q1-Q1对N-S方程进行数值求解.误差分析和数值算例结果表明,当粗、细网格尺度H=O(h1/2)时,它们与在细网格上的单层有限元算法具有相同的收敛速度,而两层算法却节省了大量的计算时间.相比之下,Simple算法具有更高的计算效率.而且进一步发现Oseen算法能够对小粘性系数N-S方程进行有效求解.