Least-squares methods for linear elasticity: refined error estimates

Fleurianne Bertrand; Henrik Schneider

doi:10.23967/wccm-eccomas.2020.137

Least-squares methods for linear elasticity: refined error estimates

Fleurianne Bertrand^*, Henrik Schneider

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

1 Citation (Scopus)

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Abstract

We consider the linear elasticity problems and compare the approximations obtained by the Least-Squares finite element method with the approximations obtained by the standard conforming finite element method and the mixed finite element method. The main result is that the H¹-conforming displacement approximations (least-squares finite element and standard finite element) as well as the H(div)-conforming stress approximations are higher-order pertubations of each other. This leads to refined a priori bounds and superconvergence results. Numerical experiments illustrate the theory.

Original language	English
Title of host publication	14th World Congress on Computational Mechanics
Subtitle of host publication	WCCM-ECCOMAS Congress 2020
Editors	F. Chinesta, R. Abgrall, O. Allix, M. Kaliske
Publisher	SCIPEDIA
Pages	1-13
Number of pages	13
Volume	800
DOIs	https://doi.org/10.23967/wccm-eccomas.2020.137
Publication status	Published - 11 Mar 2021
Event	14th World Congress of Computational Mechanics and ECCOMAS Congress, WCCM-ECCOMAS 2020 - Virtual, Online Duration: 11 Jan 2021 → 15 Jan 2021

Conference

Conference	14th World Congress of Computational Mechanics and ECCOMAS Congress, WCCM-ECCOMAS 2020
Abbreviated title	WCCM-ECCOMAS 2020
Period	11/01/21 → 15/01/21

Keywords

Least-Squares Finite Element Method
Linear elasticity

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Least-squares methodsFinal published version, 3.28 MBLicence: CC BY-NC-SA

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title = "Least-squares methods for linear elasticity: refined error estimates",

abstract = "We consider the linear elasticity problems and compare the approximations obtained by the Least-Squares finite element method with the approximations obtained by the standard conforming finite element method and the mixed finite element method. The main result is that the H1-conforming displacement approximations (least-squares finite element and standard finite element) as well as the H(div)-conforming stress approximations are higher-order pertubations of each other. This leads to refined a priori bounds and superconvergence results. Numerical experiments illustrate the theory.",

keywords = "Least-Squares Finite Element Method, Linear elasticity",

author = "Fleurianne Bertrand and Henrik Schneider",

note = "Funding Information: 1Acknowledgments: The first author gratefully acknowledge support by the Deutsche Forschungsgemeinschaft 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. Publisher Copyright: {\textcopyright} 2021, Univelt Inc., All rights reserved.; 14th World Congress of Computational Mechanics and ECCOMAS Congress, WCCM-ECCOMAS 2020, WCCM-ECCOMAS 2020 ; Conference date: 11-01-2021 Through 15-01-2021",

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doi = "10.23967/wccm-eccomas.2020.137",

language = "English",

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Bertrand, F & Schneider, H 2021, Least-squares methods for linear elasticity: refined error estimates. in F Chinesta, R Abgrall, O Allix & M Kaliske (eds), 14th World Congress on Computational Mechanics: WCCM-ECCOMAS Congress 2020. vol. 800, SCIPEDIA, pp. 1-13, 14th World Congress of Computational Mechanics and ECCOMAS Congress, WCCM-ECCOMAS 2020, 11/01/21. https://doi.org/10.23967/wccm-eccomas.2020.137

Least-squares methods for linear elasticity: refined error estimates. / Bertrand, Fleurianne; Schneider, Henrik.
14th World Congress on Computational Mechanics: WCCM-ECCOMAS Congress 2020. ed. / F. Chinesta; R. Abgrall; O. Allix; M. Kaliske. Vol. 800 SCIPEDIA, 2021. p. 1-13.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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T1 - Least-squares methods for linear elasticity

T2 - 14th World Congress of Computational Mechanics and ECCOMAS Congress, WCCM-ECCOMAS 2020

AU - Bertrand, Fleurianne

AU - Schneider, Henrik

N1 - Funding Information: 1Acknowledgments: The first author gratefully acknowledge support by the Deutsche Forschungsgemeinschaft 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. Publisher Copyright: © 2021, Univelt Inc., All rights reserved.

PY - 2021/3/11

Y1 - 2021/3/11

N2 - We consider the linear elasticity problems and compare the approximations obtained by the Least-Squares finite element method with the approximations obtained by the standard conforming finite element method and the mixed finite element method. The main result is that the H1-conforming displacement approximations (least-squares finite element and standard finite element) as well as the H(div)-conforming stress approximations are higher-order pertubations of each other. This leads to refined a priori bounds and superconvergence results. Numerical experiments illustrate the theory.

AB - We consider the linear elasticity problems and compare the approximations obtained by the Least-Squares finite element method with the approximations obtained by the standard conforming finite element method and the mixed finite element method. The main result is that the H1-conforming displacement approximations (least-squares finite element and standard finite element) as well as the H(div)-conforming stress approximations are higher-order pertubations of each other. This leads to refined a priori bounds and superconvergence results. Numerical experiments illustrate the theory.

KW - Least-Squares Finite Element Method

KW - Linear elasticity

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DO - 10.23967/wccm-eccomas.2020.137

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AN - SCOPUS:85122081798

VL - 800

SP - 1

EP - 13

BT - 14th World Congress on Computational Mechanics

A2 - Chinesta, F.

A2 - Abgrall, R.

A2 - Allix, O.

A2 - Kaliske, M.

PB - SCIPEDIA

Y2 - 11 January 2021 through 15 January 2021

ER -

Least-squares methods for linear elasticity: refined error estimates

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