Abstract: In the usual finite element method, the order of the interpolation in an element is kept unchanged, and the accuracy is raised by subdividing the grid denser and denser. Alternatively, in the large element method, the grid is kept unchanged, and the terms of approximate series in the element are increased to raise the accuracy.In this paper, a method for constructing large elements is presented. When using this method,two sets of variables, one set defined inside the element, and the other defined on the boundary of the element, are adopted. Then, these two sets of variables are combined by the hybrid-penalty function method.This method can be applied to any elliptic equations in a domain with arbitrary shape and arbitrary complex boundary condition.It is proved with strict mathematical method in this paper, that in general cases,the accuracy of this method is much higher than that of the usual element and the large element method presented in [7].Therefore,the degrees of freedom needed in this method are much fewer than those in the two methods if the same accuracy is preserved.

Key words: global attractivity, nonlinear, nonautonomous, delay difference equation