Computation of eigenvalues in linear elasticity with least-squares finite elements: dealing with the mixed system

Linda Alzaben; Fleurianne Bertrand; Daniele Boffi

doi:10.23967/wccm-eccomas.2020.095

Computation of eigenvalues in linear elasticity with least-squares finite elements: dealing with the mixed system

Linda Alzaben
, Fleurianne Bertrand
, Daniele Boffi

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

2 Citations (Scopus)

191 Downloads (Pure)

Abstract

In this paper we discuss some aspects related to the practical implementation of a method that has been introduced recently for the approximation of the eigenvalues of the linear elasticity problem. The scheme, based on a least-squares finite element formulation, gives rise to a non-symmetric discrete formulation that may have complex eigenvalues. Moreover the algebraic eigenvalue problem to be solved is singular, so that the theoretical estimates about the convergence of the scheme should be carefully interpreted.

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	1-7
Number of pages	7
Volume	700
DOIs	https://doi.org/10.23967/wccm-eccomas.2020.095
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

Eigenvalue problems
Least-squares finite elements
Linear elasticity
Mixed finite element method

Access to Document

10.23967/wccm-eccomas.2020.095Licence: CC BY-NC-SA

Computation of eigenvaluesFinal published version, 229 KBLicence: CC BY-NC-SA

Cite this

Alzaben, L., Bertrand, F., & Boffi, D. (2021). Computation of eigenvalues in linear elasticity with least-squares finite elements: dealing with the mixed system. In F. Chinesta, R. Abgrall, O. Allix, & M. Kaliske (Eds.), 14th World Congress on Computational Mechanics: WCCM-ECCOMAS Congress 2020 (Vol. 700, pp. 1-7). SCIPEDIA. https://doi.org/10.23967/wccm-eccomas.2020.095

@inproceedings{49611909c9ba4cad93181394704b43e8,

title = "Computation of eigenvalues in linear elasticity with least-squares finite elements: dealing with the mixed system",

abstract = "In this paper we discuss some aspects related to the practical implementation of a method that has been introduced recently for the approximation of the eigenvalues of the linear elasticity problem. The scheme, based on a least-squares finite element formulation, gives rise to a non-symmetric discrete formulation that may have complex eigenvalues. Moreover the algebraic eigenvalue problem to be solved is singular, so that the theoretical estimates about the convergence of the scheme should be carefully interpreted.",

keywords = "Eigenvalue problems, Least-squares finite elements, Linear elasticity, Mixed finite element method",

author = "Linda Alzaben and Fleurianne Bertrand and Daniele Boffi",

note = "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",

year = "2021",

month = mar,

day = "11",

doi = "10.23967/wccm-eccomas.2020.095",

language = "English",

volume = "700",

pages = "1--7",

editor = "F. Chinesta and R. Abgrall and O. Allix and M. Kaliske",

booktitle = "14th World Congress on Computational Mechanics",

publisher = "SCIPEDIA",

address = "Spain",

}

Alzaben, L, Bertrand, F & Boffi, D 2021, Computation of eigenvalues in linear elasticity with least-squares finite elements: dealing with the mixed system. in F Chinesta, R Abgrall, O Allix & M Kaliske (eds), 14th World Congress on Computational Mechanics: WCCM-ECCOMAS Congress 2020. vol. 700, SCIPEDIA, pp. 1-7, 14th World Congress of Computational Mechanics and ECCOMAS Congress, WCCM-ECCOMAS 2020, 11/01/21. https://doi.org/10.23967/wccm-eccomas.2020.095

Computation of eigenvalues in linear elasticity with least-squares finite elements: dealing with the mixed system. / Alzaben, Linda; Bertrand, Fleurianne; Boffi, Daniele.
14th World Congress on Computational Mechanics: WCCM-ECCOMAS Congress 2020. ed. / F. Chinesta; R. Abgrall; O. Allix; M. Kaliske. Vol. 700 SCIPEDIA, 2021. p. 1-7.

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

TY - GEN

T1 - Computation of eigenvalues in linear elasticity with least-squares finite elements

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

AU - Alzaben, Linda

AU - Bertrand, Fleurianne

AU - Boffi, Daniele

PY - 2021/3/11

Y1 - 2021/3/11

N2 - In this paper we discuss some aspects related to the practical implementation of a method that has been introduced recently for the approximation of the eigenvalues of the linear elasticity problem. The scheme, based on a least-squares finite element formulation, gives rise to a non-symmetric discrete formulation that may have complex eigenvalues. Moreover the algebraic eigenvalue problem to be solved is singular, so that the theoretical estimates about the convergence of the scheme should be carefully interpreted.

AB - In this paper we discuss some aspects related to the practical implementation of a method that has been introduced recently for the approximation of the eigenvalues of the linear elasticity problem. The scheme, based on a least-squares finite element formulation, gives rise to a non-symmetric discrete formulation that may have complex eigenvalues. Moreover the algebraic eigenvalue problem to be solved is singular, so that the theoretical estimates about the convergence of the scheme should be carefully interpreted.

KW - Eigenvalue problems

KW - Least-squares finite elements

KW - Linear elasticity

KW - Mixed finite element method

UR - https://www.scopus.com/pages/publications/85113539637

U2 - 10.23967/wccm-eccomas.2020.095

DO - 10.23967/wccm-eccomas.2020.095

M3 - Conference contribution

AN - SCOPUS:85113539637

VL - 700

SP - 1

EP - 7

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 -

Computation of eigenvalues in linear elasticity with least-squares finite elements: dealing with the mixed system

Abstract

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this