GLOBAL SUPERCONVERGENCE OF BIQUADRATIC LAGRANGE ELEMENTS FOR POISSON'S EQUATION

摘要

Biquadratic Lagrange elements are important in application, because they are used most often among high order finite element methods (FEMs). In this pa-per, we report some new discoveries of biquadratic Lagrange elements for the Dirichlet problem of Poisson's equation in error estimates and global supercon-vergences. It is well known in Ciarlet [3] that the optimal convergence rate u ~ Uhl = O(/i2|ii|3) is obtained, where u and it are the biquadratic Lagrange element solution and the true solution, respectively. In Lin, Yan and Zhou [8], the superclose ui — v,hl = O(h4||u||5) can be obtained for uniform rectangles Dy, where uj is the biquadratic Lagrange interpolant of the true solutions u.