First order least-squares formulations for eigenvalue problems

Fleurianne Herveline Bertrand; Daniele Boffi

doi:10.1093/imanum/drab005

First order least-squares formulations for eigenvalue problems

Fleurianne Herveline Bertrand, Daniele Boffi

Computer, Electrical and Mathematical Sciences and Engineering

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

8 Scopus citations

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 L2 error estimates. A priori and a posteriori estimates are proved.

Original language	English (US)
Journal	IMA Journal of Numerical Analysis
DOIs	https://doi.org/10.1093/imanum/drab005
State	Published - Mar 4 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-03-23
Acknowledgements: The first author gratefully acknowledges support by the German Research Foundation (DFG) in the Priority Programme SPP 1748 Reliable simulation techniques in solid mechanics under grant number BE6511/1-1.

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics
General Mathematics

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10.1093/imanum/drab005

https://repository.kaust.edu.sa/bitstream/10754/661770/3/drab005.pdf

Cite this

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title = "First order least-squares formulations for eigenvalue problems",

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 L2 error estimates. A priori and a posteriori estimates are proved.",

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

note = "KAUST Repository Item: Exported on 2021-03-23 Acknowledgements: The first author gratefully acknowledges support by the German Research Foundation (DFG) in the Priority Programme SPP 1748 Reliable simulation techniques in solid mechanics under grant number BE6511/1-1.",

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AU - Bertrand, Fleurianne Herveline

AU - Boffi, Daniele

N1 - KAUST Repository Item: Exported on 2021-03-23 Acknowledgements: The first author gratefully acknowledges support by the German Research Foundation (DFG) in the Priority Programme SPP 1748 Reliable simulation techniques in solid mechanics under grant number BE6511/1-1.

PY - 2021/3/4

Y1 - 2021/3/4

N2 - 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 L2 error estimates. A priori and a posteriori estimates are proved.

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 L2 error estimates. A priori and a posteriori estimates are proved.

UR - http://hdl.handle.net/10754/661770

UR - https://academic.oup.com/imajna/advance-article/doi/10.1093/imanum/drab005/6157011

U2 - 10.1093/imanum/drab005

DO - 10.1093/imanum/drab005

M3 - Article

SN - 0272-4979

JO - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

ER -

First order least-squares formulations for eigenvalue problems

Abstract

Bibliographical note

ASJC Scopus subject areas

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