What question did this study set out to answer?

To compute guaranteed lower eigenvalue bounds with hybrid high-order eigensolvers.

March 15, 2026

Lower eigenvalue bounds with hybrid high-order methods

Key Points

To compute guaranteed lower eigenvalue bounds with hybrid high-order eigensolvers.
Proposed hybrid high-order eigensolvers for lower eigenvalue bounds
Utilized adaptive mesh-refining algorithms
Analyzed convergence rates with local embeddings for all polynomial degrees.
Achieved higher-order convergence rates for lower eigenvalue bounds
Demonstrated applicability in linear elasticity problems
Utilized locally available constants for various polynomial degrees.

Abstract

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. A wide range of applications is possible, including the linear elasticity and Steklov eigenvalue problems.

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Lower eigenvalue bounds with hybrid high-order methods

Key Points

Abstract

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