The Effect Of Numerical Integration For A Nonconforming Quadrilateral Finite Element

The main aim of this paper is to study the effect of numerical integration for a non-conforming quadrilateral finite element for general second order elliptic problems. Some numerical quadrature formulas are presented and analyzed. By a novel approach, we derive a formulas with only three sampling points, which also leads to the optimal error estimate. Furthermore, the numerical experiments verify the validity of our theoretical analysis.