瞬态N-S方程的二阶全离散稳定化两重网格有限元方法  

A stabilization finite element method of second-order two-grid fully discrete model for the transient Navier-Stokes equations

作　　者：刘华蓉[1] 龙文光[2] 

机构地区：[1]四川大学数学学院,成都610064 [2]内江师范学院现代教育技术中心,内江641112

出　　处：《四川大学学报（自然科学版）》2013年第2期230-240,共11页Journal of Sichuan University(Natural Science Edition)

摘　　要：文中对瞬态N-S方程建立了一个二阶全离散稳定化两重网格有限元方法.该方法不需要有限元空间满足inf-sup条件,格式中的稳定项也与参数选取无关且无边界积分项.在实际计算时只需先在网格长度为H的粗格上解非线性N-S方程,然后在网格长度为hH的细格上解一个线性Stokes方程,仍可达到细网格上求N-S方程的逼近精度,既节约了计算内存,也提高了计算效率.如果选择适当的网格长度,则两层格式所得到的误差与标准格式的误差具有相同的精度.We consider a second-order two-grid scheme fully discrete for solving the transient Navier-Stokes equations combined with the stabilization method.This method need not satisfy the so-called inf-sup condition,and the stabilized term presents attractive features such as being parameter-free,or being defined for nonedge-based data structures.The two grid-scheme involves solving one nonlinear Navier-Stokes problem on a coarse mesh with mesh size H,one linear stokes problem on a fine mesh with mesh size hH.This method can save the calculation memory and improve the calculation efficiency.if we choose proper mesh size,then the error estimate of the two level method and the standard method have the same order.

关 键 词：两重网格算法 稳定方法 误差估计 

分 类 号：O242.21[理学—计算数学]