Lower eigenvalue bounds with hybrid high-order methods

TL;DR

This paper introduces hybrid high-order eigensolvers that provide guaranteed lower eigenvalue bounds with higher order convergence, suitable for adaptive mesh refinement, applicable to elasticity and Steklov problems.

Contribution

The paper develops new hybrid high-order methods that yield guaranteed lower eigenvalue bounds with improved convergence rates and broad applicability.

Findings

Bounds exhibit higher order convergence rates.

Constants derived from local embeddings are available for all polynomial degrees.

Applicable to linear elasticity and Steklov eigenvalue problems.

Abstract

This paper proposes hybrid high-order eigensolvers for the computation of guaranteed lower eigenvalue bounds. These bounds display higher order convergence rates and are accessible to adaptive mesh-refining algorithms. The involved constants arise from local embeddings and are available for all polynomial degrees. Applications include the linear elasticity and Steklov eigenvalue problem.