定常Navier-Stokes方程的Newton两层稳定化有限元方法

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 for the steady Navier-stokes equations

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.