In this paper, we apply combined hybrid finite element methods to the eigenvalue problems, and construct a new finite element method for solving the smallest eigenvalue. First, we derive the optimal error estimation, and then we use numerical examples to verify our theoretical results. Both theoretical analyses and numerical results show that for all the combined coefficient , our methods can obtain second order accuracy for solving the smallest eigenvalue when the lowest order finite element spaces are used. From the numerical performance, we can also observe that the numerical solution can approach to the exact eigenvalue from both directions for different , so we can choose the optimal such that better approximations can be obtained on the coarse grid.
