Lower eigenvalue bounds with hybrid high-order methods
This work addresses eigenvalue estimation in computational mathematics, particularly for linear elasticity and Steklov problems, but appears incremental as it builds on existing hybrid high-order methods.
The paper tackled the problem of computing guaranteed lower eigenvalue bounds by proposing hybrid high-order eigensolvers, achieving higher order convergence rates and compatibility with adaptive mesh-refining algorithms.
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.