Work

Comparison of guaranteed lower eigenvalue bounds with three skeletal schemes

Year: 2024

Type: article

Abstract: Specially tailored skeletal schemes enable cell and face variableslinked with a stabilisation and a fine-tuned parameter can provide guaranteedlower eigenvalue bounds for the Laplacian. This paper briefly presentsa unified derivation of skeletal higher-order methods from [Carstensen-Zhai-Zhang, SINUM 2020], [Carstensen-Ern-Puttkammer, Numer. Math. 2021], and[Carstensen-Gr¨aßle-Tran, Numer. Math. 2024]. It suggests a paradigm shiftfrom conditional to unconditional lower eigenvalue bounds. Adaptive meshrefiningleads to optimal convergence rates in computational benchmark examplesand underlines the superiority of higher-order methods.

Source: Computer Methods in Applied Mechanics and Engineering

DOI: 10.1016/j.cma.2024.117477

Authors: Carsten Carstensen, Benedikt Gräßle, Emilie Pirch

Institutions: Humboldt-Universität zu Berlin, University of Zurich, Friedrich Schiller University Jena

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,660

Funders: Deutsche Forschungsgemeinschaft, European Research Council