Superconvergent Two-grid Methods For Elliptic Eigenvalue Problems

TL;DR

This paper introduces new superconvergent two-grid algorithms for elliptic eigenvalue problems, combining multiple techniques to improve accuracy and efficiency, with theoretical analysis and numerical validation.

Contribution

It proposes novel two-grid methods that integrate shifted inverse power, two-space, and polynomial recovery techniques, achieving superconvergence for elliptic eigenvalue problems.

Findings

Algorithms outperform existing methods in accuracy

Superconvergence property is demonstrated theoretically

Numerical tests confirm improved efficiency

Abstract

Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm, two-space method, the shifted inverse power method, and the polynomial preserving recovery technique . Our new algorithms compare favorably with some existing methods and enjoy superconvergence property.