Some New Special Properties Of Projection Type Interpolation And The Interpolation's Application In High-degree Finite Elements

In this thesis, some new special properties of the projection type interpolation are studied based on the lobatto expansion of the function and the original theory of the projection type interpolation. And it is proved that the new type interpolation is the optimal interpolation in the calculus of high-degree finite elements.Firstly, a new error estimate model—pointwise error estimate of the projection type interpolation is presented. The degree of interpolation polynomial k can increase dynamically and the relation between error coefficients and k is showed accurately.Secondly, a recursive calculation method and the approximation curve of error polynomial A_k(x) are given out, which show the uniform approximation of projection type interpolation.Finally, a new result is obtained that the projection type interpolation is the optimal interpolation in the calculus of high-degree finite elements, which is verified by a numerical example for veriable coefficients two-point boundary value problem. Thus a new method for the error estimation of the finite element solution is proposed.