Navier-Stokes方程两层稳定有限元算法分析

Analysis of Two-level Stabilized Finite Element Methods for Stationary Navier-Stokes Equations

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。

In this paper,two kinds of two-level stabilized finite element methods based on local Gauss integral technique for the two-dimensional stationary 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 provide an approximate solution with the convergence rate of the same order as the usual stabilized finite 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 stabilized methods are compared in efficiency and precision aspects by a series of numerical experiments.The conclusion is that the simple two-level 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.