关于特征值问题有限元近似解的最大模估计及其校正加速估计

本文记通常CooeB空间W_p~m(Ω)(P=2时记为H~m(Ω))的模为||·||_(m,p),m=0,即空间L_p(Ω)的模简记为||·||_p。 设Ω为平面有界区域,边界?Ω分段光滑,则(1)的解存在,且特征值可列:     

MAXIMUM NORM ERROR ESTIMATES FOR FINITE ELEMENT APPROXIMATIONS OF THE STATIONARY AND NONSTATIONARY NAVIER-STOKES PROBLEMS

This paper deals with maximum norm error estimates of conforming finite element approximate solutions for the stationary and nonstationary Navier-Stokes problems in a plane bounded domain, using the so-called velocity-pressure mixed variational formulation. Quasi-optimal maximum norm error estimates of the velocity and its first derivatives, and the pressure are obtained for conforming finite element approximations of the stationary Navier-Stokes problem by some estimates of the Green function and their finite element approximations for Stokes problem. Moreover, with the method of Navier-Stokes projection, quasi-optimal maximum norm error estimate results are shown for semidiscrete conforming finite element approximations of the nonstationary Navier-Stokes problem.     

Stokes问题的区域分解法

本文主要讨论了Ｓｔｏｋｅｓ问题的非重迭型两仓区域性情形的区域分解算法，首先讨论了连续情形，然后将区域分解算法应用到Ｓｔｏｋｅｓ问题的非协调离散情形。