Spectral indicator method for a son-selfadjoint Steklov eigenvalue problem

J. Liu, Jinan University
J. Sun, Michigan Technological University
T. Turner, University of Maryland Eastern Shore

© Springer Science+Business Media, LLC, part of Springer Nature 2019. Publisher’s version of record: https://doi.org/10.1007/s10915-019-00913-6


We propose an efficient numerical method for a non-selfadjoint Steklov eigenvalue problem. The Lagrange finite element is used for discretization and the convergence is proved using the spectral perturbation theory for compact operators. The non-selfadjointness of the problem leads to non-Hermitian matrix eigenvalue problem. Due to the existence of complex eigenvalues and lack of a priori spectral information, we employ the recently developed spectral indicator method to compute eigenvalues in a given region on the complex plane. Numerical examples are presented to validate the effectiveness of the proposed method.