非协调有限元差的L~∞估计

L~∞-Estimates for Nonconforming Finite Element Approximations

引言对于区域Ω上的二阶椭园型边值问题的协调有限元近似解的误差的L~∞估计,Scott,Nitsche等得到如下的结果:

In papers[5] and [6], a method, called compensation method following[6],for using nonconforming finite elements was proposed. The order of the error of theapproximations obtained by using the method in norm ||·||_ is the same with that ofthe conforming elements with the same order piecewise polynomials. In this paper, wedeal with the L~∞--error estimates of the above approximations. For the weaklydiscontinuous finite elements with piecewise polynomials of order k-1, we get estimate: ||u-u_h||_(0, ∞)≤ch^(k-1)||u||_(k, ∞) Numerical example is also given to explain the results of the analysis.