On the Spectrum of an Operator Associated with Least-Squares Finite Elements for Linear Elasticity

Linda Alzaben; Fleurianne Bertrand; Daniele Boffi

doi:10.1515/cmam-2022-0044

On the Spectrum of an Operator Associated with Least-Squares Finite Elements for Linear Elasticity

Linda Alzaben, Fleurianne Bertrand, Daniele Boffi^*

^*Corresponding author for this work

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

2 Scopus citations

Abstract

In this paper we provide some more details on the numerical analysis and we present some enlightening numerical results related to the spectrum of a finite element least-squares approximation of the linear elasticity formulation introduced recently. We show that, although the formulation is robust in the incompressible limit for the source problem, its spectrum is strongly dependent on the Lamé parameters and on the underlying mesh.

Original language	English (US)
Pages (from-to)	511-528
Number of pages	18
Journal	Computational Methods in Applied Mathematics
Volume	22
Issue number	3
DOIs	https://doi.org/10.1515/cmam-2022-0044
State	Published - Jul 1 2022

Keywords

Eigenvalue Problem
Least-Squares Finite Elements
Linear Elasticity

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1515/cmam-2022-0044

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abstract = "In this paper we provide some more details on the numerical analysis and we present some enlightening numerical results related to the spectrum of a finite element least-squares approximation of the linear elasticity formulation introduced recently. We show that, although the formulation is robust in the incompressible limit for the source problem, its spectrum is strongly dependent on the Lam{\'e} parameters and on the underlying mesh.",

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AU - Boffi, Daniele

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Y1 - 2022/7/1

N2 - In this paper we provide some more details on the numerical analysis and we present some enlightening numerical results related to the spectrum of a finite element least-squares approximation of the linear elasticity formulation introduced recently. We show that, although the formulation is robust in the incompressible limit for the source problem, its spectrum is strongly dependent on the Lamé parameters and on the underlying mesh.

AB - In this paper we provide some more details on the numerical analysis and we present some enlightening numerical results related to the spectrum of a finite element least-squares approximation of the linear elasticity formulation introduced recently. We show that, although the formulation is robust in the incompressible limit for the source problem, its spectrum is strongly dependent on the Lamé parameters and on the underlying mesh.

KW - Eigenvalue Problem

KW - Least-Squares Finite Elements

KW - Linear Elasticity

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M3 - Article

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On the Spectrum of an Operator Associated with Least-Squares Finite Elements for Linear Elasticity

Abstract

Keywords

ASJC Scopus subject areas

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