【摘要】 讨论分析了定常Navier-Stokes（N-S）方程的三种两层稳定有限元算法.它们将局部高斯积分稳定化技术和两层算法的思想充分结合,采用不满足Inf-Sup条件的低次等价有限元P₁-P₁或Q₁-Q₁对N-S方程进行数值求解,在粗网格上解定常N-S方程,在细网格上只需求解一个Stokes方程.误差分析和数值实验都表明,当它们的粗、细网格尺度比分别为H=h^1/3| logh|^-1/6,H=O(h^1/2)和H=O(h^1/2)时,它们与在细网格上的标准有限元算法具有相同的收敛速度.而两层稳定有限元算法却节省了大量的计算时间.相比之下,简单两层稳定有限元算法具有更高的计算效率,Oseen两层算法次之,Newton两层算法较低而且进一步发现较小粘性系数对Newton两层算法数值精度影响较大.更多还原

【Abstract】 In this paper,three 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 while do not satisfy the inf-sup condion are considered.The two-level methods consist of solving a small non-linear system on the coarse mesh and then solving a linear system on the fine mesh.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=h^1/3|logh|^-1/6,H=O(h^1/2)and H=O(h^1/2)Therefore,the two-level methods are of practical importance in scientific computation.Finally,the performance of three 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 others in accuracy and efficiency.And,there is poor numerical accuracy for the Newton algorithm to N-S equations with low viscosity coefficient.更多还原