For the eigenvalue problem of the Steklov differential operator, by following Liu's approach, an algorithm utilizing the conforming finite element method (FEM) is proposed to provide guaranteed lower bounds for the eigenvalues. The proposed method requires the a priori error estimation for FEM solution to nonhomogeneous Neumann problems, which is solved by constructing the hypercircle for the corresponding FEM spaces and boundary conditions. Numerical examples are also shown to confirm the efficiency of our proposed method.

翻译：对于Steklov差价操作员的异常值问题,建议采用刘氏的方法,使用符合的有限元素法(FEM)进行算法,为乙基值提供有保证的下限界限。拟议方法要求对FEM的非同源性内纽曼问题的解决办法进行先验误差估计,通过为相应的FEM空格和边界条件建造双环来解决这个问题。数字例子也证实了我们拟议方法的效率。