TWO FAMILIES OF n-RECTANGLE NONCONFORMING FINITE ELEMENTS FOR SIXTH-ORDER ELLIPTIC EQUATIONS  

作　　者：Xianlin Jin Shuonan Wu 

机构地区：[1]School of Mathematical Sciences,Peking University,Beijing 100871,China

出　　处：《Journal of Computational Mathematics》2025年第1期121-142,共22页计算数学(英文)

基　　金：supported in part by the National Natural Science Foundation of China(Grant No.12222101).

摘　　要：In this paper, we propose two families of nonconforming finite elements on n-rectangle meshes of any dimension to solve the sixth-order elliptic equations. The unisolvent property and the approximation ability of the new finite element spaces are established. A new mechanism, called the exchange of sub-rectangles, for investigating the weak continuities of the proposed elements is discovered. With the help of some conforming relatives for the H^(3) problems, we establish the quasi-optimal error estimate for the triharmonic equation in the broken H^(3) norm of any dimension. The theoretical results are validated further by the numerical tests in both 2D and 3D situations.

关 键 词：Nonconforming finite element method n-Rectangle element Sixth-order elliptic equation Exchange of sub-rectangles 

分 类 号：O17[理学—数学]