Guaranteed Lower Eigenvalue Bounds for Steklov Operators Using Conforming Finite Element Methods

Abstract

Abstract For the eigenvalue problem of the Steklov differential operator, an algorithm based on the conforming finite element method (FEM) is proposed to provide guaranteed lower bounds for the eigenvalues. The proposed lower eigenvalue bounds utilize the a priori error estimation for FEM solutions to non-homogeneous Neumann boundary value problems, which is obtained by constructing the hypercircle for the corresponding FEM spaces and boundary conditions. Numerical examples demonstrate the efficiency of our proposed method.