Tetrahedron Isoparametric Element Interpolation Error Analysis And Order Problem

The convergence of tetrahedral isoparametric element is analysed in this paper, and the optimal H~1 error estimate is obtained,then it is used to solve 3-dimensional 2-order homogeneous Dirichlet problem on surface domain.As the reversibility of isoparametric transformation is always supposed to be true in published papers, in this thesis, a kind of realizability of the reversibility is proposed.When the stiffness matrix and load vector of isoparametric element are determined, the transformation between general unit K and standard unit K is nonlinear, so it's difficult to calculate. For the simplicity of calculation, a kind of numerical integration format is constructed, and its convergence is proved later. After compared the correspondent numerical integration format of two and three dimention, it's concluded that many numerical integration formats which are true in two dimention may be false in three dimention.