Solving Elliptic Problems In Domain By A High Order Scheme Of Hermite Finite Element

In this paper, first we study the basic theory of the finite element methods, then we consider a 24 rectangular element to solve the fourth-order problem,obtain the error estimations in theory, and give an numerical example to demonstrate the result of our theoretical analysis. In the last sec-tion,we expand the element to three dimension further,that's the 80 cubic element. The advantage of the two element is that we can directly obtain the second derivatives of the function, especially in solving the problem about multi-scale.