A Spectral Element Method for Second-order Elliptic Intersection Problem

In this paper, the spectral element method for one-dimensional second-order interface elliptic problem is given. First, the corresponding Sobolev space is defined and established variational form and its discrete scheme. Secondly, the existence and uniqueness of the weak solution and its approximate solution are proved theoretically. In addition, the implementation process of the algorithm is described in detail, and a large number of numerical examples are given to prove the advantages of our algorithm. The results show that the algorithm can achieve excellent convergence and ultra-high precision for interface problems.