定常Navier-Stokes方程低阶混合有限元的压力投影稳定化方法

Stabilization of the Lowest-order Mixed Finite Elements Based on the Local Pressure Projection for Steady Navier-Stokes Equations

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稳定化有限元方法。与其它的稳定化方法相比,稳定项不需要介入稳定化参数,不用进行高阶导数的运算,或者边界积分,稳定在局部单元上进行,且容易编程实现。针对稳定化有限元逼近解,证明了最优的误差估计。数值实验表明,该方法有很好的稳定性和收敛性。

pressure projection for the steady Navier-Stokes equations by the lowest order conforming finite element pairs （i.e. Q1 - Po; P1 - P0）. In contrast to other stabilized methods, the new method is parameter free, it is not neces- sary to calculate higher order derivatives and edge-based data structures, and it is implemented at the element level with minimal cost. For the stabilized finite element solution, the optimal error estimates have been obtained. Finally, the numerical examples demonstrate the better stability and convergence of the stabilized finite element method for the Navier-Stokes equations.