The Shifted-inverse Power Weak Galerkin Method for Eigenvalue Problems

TL;DR

This paper introduces a novel weak Galerkin method utilizing the shifted-inverse power technique to efficiently compute eigenvalues with high accuracy and lower bounds, supported by theoretical analysis and numerical validation.

Contribution

It presents a new weak Galerkin approach with shifted-inverse power for eigenvalue problems, providing high order lower bounds at reduced computational cost.

Findings

High order lower bounds achieved efficiently

Error estimates for eigenvalues and eigenfunctions derived

Numerical results confirm theoretical predictions

Abstract

This paper proposes and analyzes a new weak Galerkin method for the eigenvalue problem by using the shifted-inverse power technique. A high order lower bound can be obtained at a relatively low cost via the proposed method. The error estimates for both eigenvalue and eigenfunction are provided and asymptotic lower bounds are shown as well under some conditions. Numerical examples are presented to validate the theoretical analysis.