定常Navier-Stokes方程的Newton两层稳定化有限元方法  

A Newton two-level stabilized finite element method for the steady Navier-stokes equations

作　　者：王爱文[1] 黄静静[1] 

机构地区：[1]北京信息科技大学理学院,北京100192

出　　处：《北京信息科技大学学报（自然科学版）》2011年第5期25-29,共5页Journal of Beijing Information Science and Technology University

基　　金：北京市教委科技面上资助项目(KM201110772019);北京信息科技大学基金项目(5026010954)

摘　　要：针对低阶协调有限元对Q1-P0,P1-P0,对二维定常不可压缩Navier-Stokes方程,提出了建立在局部压力投影上的一类Newton两层稳定化有限元方法。在网格尺度为H的粗网格上,求解一个小型的非线性Navier-Stokes问题,在网格尺度为h的细网格上,求解一个大型的Stokes问题,如果选取h=O(│lg1/h│1/2H3),则Newton两层稳定化有限元方法和通常在细网格上求解大型Navier-Stokes方程的稳定化有限元方法有着相同的收敛精度,但是Newton两层稳定化方法更简单。A Newton two-level stabilized finite element method is investigated based on the local pressure projection for the steady Navier-Stokes equations by the lowest order conforming finite element pairs Q1-P0 and P1-P0.The Newton two-level method involves solving one small nonlinear Navier-Stokes problem on the coarse mesh with mesh size H,and a large stokes problem on the fine mesh with mesh size h.If we choose h=O（│lg1/h│1/2H3）,the Newton two-level stabilized method provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solutions,which involves solving a large Navier-Stokes problem on a fine mesh with mesh size h.But our the proposed method is more simplesimpler.

关 键 词：NAVIER-STOKES方程 稳定化有限元 局部压力投影 

分 类 号：O241.82[理学—计算数学]