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

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

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 (US)
Title of host publication	14th WCCM-ECCOMAS Congress
Publisher	CIMNE
Pages	1-10
Number of pages	10
DOIs	https://doi.org/10.23967/wccm-eccomas.2020.314
State	Published - 2021

Bibliographical note

KAUST Repository Item: Exported on 2022-01-11
Acknowledgements: 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.

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10.23967/wccm-eccomas.2020.314

https://repository.kaust.edu.sa/bitstream/10754/674893/1/Draft_Content_539319986p4724.pdf

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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.",

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

note = "KAUST Repository Item: Exported on 2022-01-11 Acknowledgements: 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.",

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doi = "10.23967/wccm-eccomas.2020.314",

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AU - Bertrand, Fleurianne

AU - Boffi, Daniele

AU - Gedicke, Joscha

AU - Khan, Arbaz

N1 - KAUST Repository Item: Exported on 2022-01-11 Acknowledgements: 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.

PY - 2021

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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.

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DO - 10.23967/wccm-eccomas.2020.314

M3 - Conference contribution

SP - 1

EP - 10

BT - 14th WCCM-ECCOMAS Congress

PB - CIMNE

ER -

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

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