Mixed Interpolation Method And Application

The finite element method is a very powerful means of approximating the solutions of partial differential equations over finite dimensional subspaces. The general method is to use piecewise polynomials spaces to approximate the finite dimensional subspaces. However, if there are too many the degrees of freedom of the nodes, the dimensional of polynomials spaces will be very high. Therefore, it's necessary to supply some other functions to keep with the continuation. In the book of Cialet, construct C~1 element by supplying rational functions. In this paper, supply trigonometric functions to construct the high order elements which contain second derivatives as the degrees of freedom. It can apply to solve the homogeneous problems and the asymptotic extension of small periodic composite materials.