Two Kinds Of Nonconforming Finite Element Method

The first part of this paper is to employ a special nonconforming finite element to derive a nonconventional quadrature integral formula with few points and high algebraic accuracy. The corresponding complex formula's convergence order is proved under weak condition by new analysis method. This formula saves about 25% computing cost compared to Simpson's formula and Gauss's formula. At last, numerical experiments are given for comparison.In the second part, we focus on the study of the application of H¹-Galerkin mixed finite element methods for telegraph equations. We study the case when the approximation spaces are the conforming Q₁ element and nonconforming C-R type rectangular element. By means of the novel techniques and the typical characteristics of the element, the same error estimation of the energy norm and L²-norm as the classical methods are obtained without requiring the Ritz projection. Thus the mixed finite element method application scope is extended.