Navier-Stokes方程的低阶混合有限元方法  

A LOW-ORDER STABILIZED MIXED FINITE ELEMENTS METHOD FOR THE NAVIER-STOKES EQUATIONS

作　　者：张莉[1] 冯民富[2] 

机构地区：[1]四川师范大学数学与软件科学学院,成都610066 [2]四川大学数学学院,成都610064

出　　处：《高等学校计算数学学报》2009年第2期97-108,共12页Numerical Mathematics A Journal of Chinese Universities

基　　金：四川省科技攻关课题(编号:05GG006-006-2)资助项目

摘　　要：定常N—S方程是流体力学中一类非常重要的方程，而经典的混合有限元方法要求有限元空间组合满足B—B条件．这一条件限制了工程中常用的低阶有限元空间如：P1／P1，P1／P0等．为了去掉LBB条件限制，产生了一种新的方法--稳定化方法（也成CBB方法）．1988年，F．Brezzi和J．Douglas．Jr对线性的Stokes方程建立了一种稳定化格式（【2】）．对于低阶的有限元应用压力投影稳定项构造了一种稳定化格式，并给出了格式的解存在唯一性，In this paper, a new stabilized method is proposed for the Navier- Stokes problems, motivated by the pressure projections and LES type finite element methods. The pressure projection stabilization is added to circumvent the LBB condition. On the other hand, when the Reynolds number grows higher, the advection term is much stronger than the diffusive one. The Navier-Stokes problem shows advection-dominated problems. The new stabilization is added for stabilizing the convection term. Without requiring the B-B stability condition, the existence and uniqueness of the discrete solution are proved by the linearized technique and the Brouwer＇s fixed point theorem, and optimal error bound is derived. In contrast to other stabilization procedures, the advantages of the new method do not require calculation of second order derivatives.

关 键 词：STOKES方程 混合有限元方法 低阶 稳定化方法 DOUGLAS 有限元空间 存在唯一性 流体力学 

分 类 号：O357.1[理学—流体力学] O175.2[理学—力学]