The Finite Element Method Of A Class Of Elliptic Boundary Value Problem

The finite element method of solving a class of the elliptic boundary value problem is discussed in this paper.This kind of elliptic equations have periodic boundary conditions. First, multiple-scale asymptotic expansion is done with the two kinds of equations namely the elliptic equation and the heat equation of periodic composite materials. Second,the finite element method is used to solve the auxiliary function equations which is in the process of asymptotic expansion,and the numerical solution of the auxiliary function can be obtained through a numerical example. Finally,the above results of the auxiliary function is used to find out the coefficients of the corresponding homogenized equation.