A New Nonconforming Pyramid Element

As a numerical analysis method for approximate differential equations,the finite element method is widely used in mathematics and engineering.In modern times,with the rapid development of computer technology,fimite element analysis has developed into a more mature theory application system.As an important finite element analysis method,the non-coordination elementsolves the problem that the coordination element needs to construct a large number of parameters while providing an effective numerical solution for the differential equation in mechanics.In this paper,a new nonparametric nonconforming pyramid finite element is introduced.This element takes the five face mean values as the degrees of the freedom and the finite element space is a subspace of P2.Different from the other nonparametric elements,the basis functions of this new element can be expressed explicitly without solving linear systems locally,which can be achieved by introducing a new reference pyramid.To evaluate the integration,a class of new quadrature formulae with only two/three equally weighted points on pyramid are constructed,and the numerical method for the realization of 3D pyramid elements has been presented.Numerical results are shown to confirm the optimality of the convergence order for the second order elliptic problems.