Comparison of guaranteed lower eigenvalue bounds with three

被引：0

作者：

Carstensen, Carsten ^{[1
]}

Graessle, Benedikt ^{[2
]}

Pirch, Emilie ^{[3
]}

机构：

[1] Humboldt Univ, Inst Math, D-10117 Berlin, Germany

[2] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland

[3] Friedrich Schiller Univ Jena, Inst Math, D-07743 Jena, Germany

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2025年 / 433卷

关键词：

A posteriori error control; Eigenvalues; Guaranteed lower bounds; Adaptive algorithm; Competition; Higher order; HHO; Weak Galerkin; HDG;

D O I：

10.1016/j.cma.2024.117477

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

Specially tailored skeletal schemes enable cell and face variables linked with a stabilisation and a fine-tuned parameter can provide guaranteed lower eigenvalue bounds for the Laplacian. This paper briefly presents a unified derivation of skeletal higher-order methods from Carstensen, Zhai, and Zhang (2020), Carstensen, Ern, and Puttkammer (2021), and Carstensen, Gr & auml;ss le, and Tran (2024). It suggests a paradigm shift from conditional to unconditional lower eigenvalue bounds. Adaptive mesh-refining leads to optimal convergence rates in computational benchmark examples and underlines the superiority of higher-order methods.

引用

页数：15

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