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March 15, 2026IMA Journal of Numerical Analysis0 citations

Lower eigenvalue bounds with hybrid high-order methods

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NTNgoc Tien Tran

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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Cite This Study

Ngoc Tien Tran (2025) studied this question.

synapsesocial.com/papers/69b5ff3b83145bc643d1b5a1https://doi.org/10.1093/imanum/draf148
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