First order least-squares formulations for eigenvalue problems

Fleurianne Bertrand; Daniele Boffi

doi:10.1093/imanum/drab005

First order least-squares formulations for eigenvalue problems

Fleurianne Bertrand, Daniele Boffi^*

^*Corresponding author for this work

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Abstract

In this paper we discuss spectral properties of operators associated with the least-squares finite-element approximation of elliptic partial differential equations. The convergence of the discrete eigenvalues and eigenfunctions towards the corresponding continuous eigenmodes is studied and analyzed with the help of appropriate $L^2$ error estimates. A priori and a posteriori estimates are proved.

Original language	English
Pages (from-to)	1339–1363
Number of pages	25
Journal	IMA Journal of Numerical Analysis
Volume	42
Issue number	2
Early online date	4 Mar 2021
DOIs	https://doi.org/10.1093/imanum/drab005
Publication status	Published - Apr 2022

Keywords

UT-Hybrid-D

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10.1093/imanum/drab005Licence: CC BY

Bertrand-2021-FirstFinal published version, 557 KBLicence: CC BY

10 Citations
1 Working paper

First order least-squares formulations for eigenvalue problems
Bertrand, F. & Boffi, D., 19 Feb 2020, Ithaca, NY: ArXiv.org, 20 p.
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AB - In this paper we discuss spectral properties of operators associated with the least-squares finite-element approximation of elliptic partial differential equations. The convergence of the discrete eigenvalues and eigenfunctions towards the corresponding continuous eigenmodes is studied and analyzed with the help of appropriate $L^2$ error estimates. A priori and a posteriori estimates are proved.

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First order least-squares formulations for eigenvalue problems

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First order least-squares formulations for eigenvalue problems

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