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 ...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.展开更多
基金supported in part by the National Natural Science Foundation of China(Grant No.12222101).
文摘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.
