Direct Guaranteed Lower Eigenvalue Bounds with Optimal a Priori Convergence Rates for the Bi-Laplacian

Carstensen, Carsten; Puttkammer, Sophie

doi:10.1137/21m139921x

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2023

2024

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Cited by 6 publications

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“…A direct computation shows that the difference of λ and the lower bound cannot be of a better order than O(δ 2 ). For the Laplacian, this limitation was recently overcome by [11], but the argument again uses particular properties of related finite element spaces and seems to be less universal. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Mixed methods and lower eigenvalue bounds

Gallistl

2023

Math. Comp.

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It is shown how mixed finite element methods for symmetric positive definite eigenvalue problems related to partial differential operators can provide guaranteed lower eigenvalue bounds. The method is based on a classical compatibility condition (inclusion of kernels) of the mixed scheme and on local constants related to compact embeddings, which are often known explicitly. Applications include scalar second-order elliptic operators, linear elasticity, and the Steklov eigenvalue problem.

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Section: Introductionmentioning

confidence: 99%