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：针对Steklov微分算子的特征值问题，本文遵循Liu的方法，提出了一种利用协调有限元方法（FEM）提供特征值严格下界的算法。该方法需要先验估计非齐次Neumann问题有限元解的误差，通过构建对应有限元空间和边界条件的超圆来解决。最后给出数值算例验证所提方法的有效性。