Three-dimensional Non-coordination Unit In The Subdivision Significance Convergence Analysis

In this paper, we mainly study the convergences of a class of noncon-forming finite element with nine parameters in 3-dimension space under three kinds of subdivision.Firstly, under the conventional regular assump-tion(refer to [1]),based on a nonconforming element with five parameters in 2-dimension space(refer to [2,3,4]) ,a noncomforning finite element with nine parameters in 3-dimension space is constructed .By the thinking of [5,6,7],we can prove that it is convergence for arbitrary convex hexahedron subdivision in 3-dimension space and its error estimate is obtained. Next,by the use of the method on anisotropy subdivision in [8],we have proved the properly advanced element satisfy the feature of anisotropy for arbitrary convex cuboid subdivision in 3-dimension space and the error estimate is obtained.Finally,relying on the thinking of the reference[9],using the similar method with [10,11], we have proved the more advanced element satisfy the feature of anisotropy for arbitrary convex hexahedron subdivision in 3-dimension space and the error estimate is obtained.