This paper introduces the application of the weak Galerkin (WG) finite element method to solve the Steklov eigenvalue problem, focusing on obtaining lower bounds of the eigenvalues. The noncomforming finite element space of the weak Galerkin finite element method is the key to obtain lower bounds of the eigenvalues. The arbitary high order lower bound estimates are given and the guaranteed lower bounds of the eigenvalues are also discussed. Numerical results demonstrate the accuracy and lower bound property of the numerical scheme.

翻译：本文介绍了弱伽辽金（WG）有限元方法在求解Steklov特征值问题中的应用，重点在于获取特征值的下界。弱伽辽金有限元方法的非协调有限元空间是获得特征值下界的关键。本文给出了任意高阶的下界估计，并讨论了特征值的可保证下界。数值结果验证了该数值格式的准确性与下界性质。