Some remarks on the a posteriori error analysis of the mixed laplace eigenvalue problem

Fleurianne Bertrand; Daniele Boffi; Joscha Gedicke; Arbaz Khan

doi:10.23967/wccm-eccomas.2020.314

Some remarks on the a posteriori error analysis of the mixed laplace eigenvalue problem

Fleurianne Bertrand
, Daniele Boffi
, Joscha Gedicke
, Arbaz Khan

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

1 Citation (Scopus)

74 Downloads (Pure)

Abstract

In this note we consider the a posteriori error analysis of mixed finite element approximations to the Laplace eigenvalue problem based on local postprocessing. The estimator makes use of an improved L² approximation for the Raviart-Thomas (RT) and Brezzi-Douglas-Marini (BDM) finite element methods. For the BDM method we also obtain improved eigenvalue convergence for postprocessed eigenvalues. We verify the theoretical results in several numerical examples.

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	1-10
Number of pages	10
Volume	700
DOIs	https://doi.org/10.23967/wccm-eccomas.2020.314
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

A posteriori error estimator
Adaptivity
Eigenvalue problem
Mixed finite element method
Postprocessing

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10.23967/wccm-eccomas.2020.314Licence: CC BY-NC-SA

Some remarksFinal published version, 404 KBLicence: CC BY-NC-SA

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title = "Some remarks on the a posteriori error analysis of the mixed laplace eigenvalue problem",

abstract = "In this note we consider the a posteriori error analysis of mixed finite element approximations to the Laplace eigenvalue problem based on local postprocessing. The estimator makes use of an improved L2 approximation for the Raviart-Thomas (RT) and Brezzi-Douglas-Marini (BDM) finite element methods. For the BDM method we also obtain improved eigenvalue convergence for postprocessed eigenvalues. We verify the theoretical results in several numerical examples.",

keywords = "A posteriori error estimator, Adaptivity, Eigenvalue problem, Mixed finite element method, Postprocessing",

author = "Fleurianne Bertrand and Daniele Boffi and Joscha Gedicke and Arbaz Khan",

note = "Funding Information: Fleurianne Bertrand 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. Daniele Boffi is member of the INdAM Research group GNCS and his research is partially supported by IMATI/CNR and by PRIN/MIUR. Arbaz Khan has been supported by the faculty initiation grant MTD/FIG/100878 and Serb Matrics grant MTR/2020/000303. 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.2020.314",

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Bertrand, F, Boffi, D, Gedicke, J & Khan, A 2021, Some remarks on the a posteriori error analysis of the mixed laplace eigenvalue problem. in F Chinesta, R Abgrall, O Allix & M Kaliske (eds), 14th World Congress on Computational Mechanics: WCCM-ECCOMAS Congress 2020. vol. 700, SCIPEDIA, pp. 1-10, 14th World Congress of Computational Mechanics and ECCOMAS Congress, WCCM-ECCOMAS 2020, 11/01/21. https://doi.org/10.23967/wccm-eccomas.2020.314

Some remarks on the a posteriori error analysis of the mixed laplace eigenvalue problem. / Bertrand, Fleurianne; Boffi, Daniele; Gedicke, Joscha et al.
14th World Congress on Computational Mechanics: WCCM-ECCOMAS Congress 2020. ed. / F. Chinesta; R. Abgrall; O. Allix; M. Kaliske. Vol. 700 SCIPEDIA, 2021. p. 1-10.

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

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AU - Boffi, Daniele

AU - Gedicke, Joscha

AU - Khan, Arbaz

N1 - Funding Information: Fleurianne Bertrand 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. Daniele Boffi is member of the INdAM Research group GNCS and his research is partially supported by IMATI/CNR and by PRIN/MIUR. Arbaz Khan has been supported by the faculty initiation grant MTD/FIG/100878 and Serb Matrics grant MTR/2020/000303. Publisher Copyright: © 2021, Univelt Inc., All rights reserved.

PY - 2021/3/11

Y1 - 2021/3/11

N2 - In this note we consider the a posteriori error analysis of mixed finite element approximations to the Laplace eigenvalue problem based on local postprocessing. The estimator makes use of an improved L2 approximation for the Raviart-Thomas (RT) and Brezzi-Douglas-Marini (BDM) finite element methods. For the BDM method we also obtain improved eigenvalue convergence for postprocessed eigenvalues. We verify the theoretical results in several numerical examples.

AB - In this note we consider the a posteriori error analysis of mixed finite element approximations to the Laplace eigenvalue problem based on local postprocessing. The estimator makes use of an improved L2 approximation for the Raviart-Thomas (RT) and Brezzi-Douglas-Marini (BDM) finite element methods. For the BDM method we also obtain improved eigenvalue convergence for postprocessed eigenvalues. We verify the theoretical results in several numerical examples.

KW - A posteriori error estimator

KW - Adaptivity

KW - Eigenvalue problem

KW - Mixed finite element method

KW - Postprocessing

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DO - 10.23967/wccm-eccomas.2020.314

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AN - SCOPUS:85122062122

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A2 - Abgrall, R.

A2 - Allix, O.

A2 - Kaliske, M.

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

Y2 - 11 January 2021 through 15 January 2021

ER -

Some remarks on the a posteriori error analysis of the mixed laplace eigenvalue problem

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