An adaptive algorithm based on the shifted inverse iteration for the Steklov eigenvalue problem

TL;DR

This paper introduces an adaptive shifted inverse iteration algorithm for the Steklov eigenvalue problem, utilizing a posteriori error estimates to improve finite element discretization accuracy, demonstrated through numerical experiments.

Contribution

It develops a new adaptive algorithm based on a posteriori error estimates for the Steklov eigenvalue problem, enhancing computational efficiency.

Findings

The proposed adaptive algorithm outperforms non-adaptive methods.

Numerical experiments confirm the efficiency of the adaptive approach.

The method effectively improves eigenvalue approximation accuracy.

Abstract

This paper proposes and analyzes an a posteriori error estimator for the finite element multi-scale discretization approximation of the Steklov eigenvalue problem. Based on the a posteriori error estimates, an adaptive algorithm of shifted inverse iteration type is designed. Finally, numerical experiments comparing the performances of three kinds of different adaptive algorithms are provided, which illustrate the efficiency of the adaptive algorithm proposed here.