Least-squares formulations for eigenvalue problems associated with linear elasticity

Fleurianne Herveline Bertrand; Daniele Boffi

doi:10.1016/j.camwa.2020.12.013

Least-squares formulations for eigenvalue problems associated with linear elasticity

Fleurianne Herveline Bertrand, Daniele Boffi

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We study the approximation of the spectrum of least-squares operators arising from linear elasticity. We consider a two-field (stress/displacement) and a three-field (stress/displacement/vorticity) formulation; other formulations might be analyzed with similar techniques. We prove a priori estimates and we confirm the theoretical results with simple two-dimensional numerical experiments.

Original language	English (US)
Journal	Computers and Mathematics with Applications
DOIs	https://doi.org/10.1016/j.camwa.2020.12.013
State	Published - Feb 15 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-03-05
Acknowledgements: The first author gratefully acknowledges support by the Deutsche Forschungsgemeinschaft, Germany in the Priority Program SPP 1748 Reliable simulation techniques in solid mechanics, Development of non standard discretization methods, mechanical and mathematical analysis under the project number BE 6511/1-1.The second author is member of the INdAM Research group GNCS and his research is partially supported by IMATI/CNR and by PRIN/MIUR.

ASJC Scopus subject areas

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

Access to Document

10.1016/j.camwa.2020.12.013

https://repository.kaust.edu.sa/bitstream/10754/667863/1/1-s2.0-S0898122120304831-main.pdf

Cite this

@article{0105a7b3ea4a48cfa9906e45aa39fb11,

title = "Least-squares formulations for eigenvalue problems associated with linear elasticity",

abstract = "We study the approximation of the spectrum of least-squares operators arising from linear elasticity. We consider a two-field (stress/displacement) and a three-field (stress/displacement/vorticity) formulation; other formulations might be analyzed with similar techniques. We prove a priori estimates and we confirm the theoretical results with simple two-dimensional numerical experiments.",

author = "Bertrand, {Fleurianne Herveline} and Daniele Boffi",

note = "KAUST Repository Item: Exported on 2021-03-05 Acknowledgements: The first author gratefully acknowledges support by the Deutsche Forschungsgemeinschaft, Germany in the Priority Program SPP 1748 Reliable simulation techniques in solid mechanics, Development of non standard discretization methods, mechanical and mathematical analysis under the project number BE 6511/1-1.The second author is member of the INdAM Research group GNCS and his research is partially supported by IMATI/CNR and by PRIN/MIUR.",

year = "2021",

month = feb,

day = "15",

doi = "10.1016/j.camwa.2020.12.013",

language = "English (US)",

journal = "Computers and Mathematics with Applications",

issn = "0898-1221",

publisher = "Elsevier",

}

TY - JOUR

T1 - Least-squares formulations for eigenvalue problems associated with linear elasticity

AU - Bertrand, Fleurianne Herveline

AU - Boffi, Daniele

N1 - KAUST Repository Item: Exported on 2021-03-05 Acknowledgements: The first author gratefully acknowledges support by the Deutsche Forschungsgemeinschaft, Germany in the Priority Program SPP 1748 Reliable simulation techniques in solid mechanics, Development of non standard discretization methods, mechanical and mathematical analysis under the project number BE 6511/1-1.The second author is member of the INdAM Research group GNCS and his research is partially supported by IMATI/CNR and by PRIN/MIUR.

PY - 2021/2/15

Y1 - 2021/2/15

N2 - We study the approximation of the spectrum of least-squares operators arising from linear elasticity. We consider a two-field (stress/displacement) and a three-field (stress/displacement/vorticity) formulation; other formulations might be analyzed with similar techniques. We prove a priori estimates and we confirm the theoretical results with simple two-dimensional numerical experiments.

AB - We study the approximation of the spectrum of least-squares operators arising from linear elasticity. We consider a two-field (stress/displacement) and a three-field (stress/displacement/vorticity) formulation; other formulations might be analyzed with similar techniques. We prove a priori estimates and we confirm the theoretical results with simple two-dimensional numerical experiments.

UR - http://hdl.handle.net/10754/667863

UR - https://linkinghub.elsevier.com/retrieve/pii/S0898122120304831

UR - http://www.scopus.com/inward/record.url?scp=85101350700&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2020.12.013

DO - 10.1016/j.camwa.2020.12.013

M3 - Article

SN - 0898-1221

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

ER -

Least-squares formulations for eigenvalue problems associated with linear elasticity

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this