| Abstract: | 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. We present the error estimation in the presence of quadrature formulae. Numerical results are shown to confirm the optimality of the convergence order for the second order elliptic problems. |
