Discontinuous Petrov–Galerkin Approximation of Eigenvalue Problems

Fleurianne Bertrand; Daniele Boffi; Henrik Schneider

doi:10.1515/cmam-2022-0069

Discontinuous Petrov–Galerkin Approximation of Eigenvalue Problems

Fleurianne Bertrand, Daniele Boffi, Henrik Schneider

Computer, Electrical and Mathematical Sciences and Engineering

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

3 Scopus citations

Abstract

In this paper, the discontinuous Petrov–Galerkin approximation of the Laplace eigenvalue problem is discussed. We consider in particular the primal and ultraweak formulations of the problem and prove the convergence together with a priori error estimates. Moreover, we propose two possible error estimators and perform the corresponding a posteriori error analysis. The theoretical results are confirmed numerically, and it is shown that the error estimators can be used to design an optimally convergent adaptive scheme.

Original language	English (US)
Journal	Computational Methods in Applied Mathematics
DOIs	https://doi.org/10.1515/cmam-2022-0069
State	Published - May 26 2022

Bibliographical note

KAUST Repository Item: Exported on 2022-05-30
Acknowledgements: The first author gratefully acknowledge support by the DFG in the Priority Program SPP 1748 Reliable simulation techniques in solid mechanics, Development of non-standard discretization methods, mechanical and mathematical analysis under the project number BE 6511/1-1. The second author is member of the INdAM Research group GNCS and his research is partially supported by IMATI/CNR and by PRIN/MIUR.

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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title = "Discontinuous Petrov–Galerkin Approximation of Eigenvalue Problems",

abstract = "In this paper, the discontinuous Petrov–Galerkin approximation of the Laplace eigenvalue problem is discussed. We consider in particular the primal and ultraweak formulations of the problem and prove the convergence together with a priori error estimates. Moreover, we propose two possible error estimators and perform the corresponding a posteriori error analysis. The theoretical results are confirmed numerically, and it is shown that the error estimators can be used to design an optimally convergent adaptive scheme.",

author = "Fleurianne Bertrand and Daniele Boffi and Henrik Schneider",

note = "KAUST Repository Item: Exported on 2022-05-30 Acknowledgements: The first author gratefully acknowledge support by the DFG in the Priority Program SPP 1748 Reliable simulation techniques in solid mechanics, Development of non-standard discretization methods, mechanical and mathematical analysis under the project number BE 6511/1-1. The second author is member of the INdAM Research group GNCS and his research is partially supported by IMATI/CNR and by PRIN/MIUR.",

year = "2022",

month = may,

day = "26",

doi = "10.1515/cmam-2022-0069",

language = "English (US)",

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T1 - Discontinuous Petrov–Galerkin Approximation of Eigenvalue Problems

AU - Bertrand, Fleurianne

AU - Boffi, Daniele

AU - Schneider, Henrik

N1 - KAUST Repository Item: Exported on 2022-05-30 Acknowledgements: The first author gratefully acknowledge support by the DFG in the Priority Program SPP 1748 Reliable simulation techniques in solid mechanics, Development of non-standard discretization methods, mechanical and mathematical analysis under the project number BE 6511/1-1. The second author is member of the INdAM Research group GNCS and his research is partially supported by IMATI/CNR and by PRIN/MIUR.

PY - 2022/5/26

Y1 - 2022/5/26

N2 - In this paper, the discontinuous Petrov–Galerkin approximation of the Laplace eigenvalue problem is discussed. We consider in particular the primal and ultraweak formulations of the problem and prove the convergence together with a priori error estimates. Moreover, we propose two possible error estimators and perform the corresponding a posteriori error analysis. The theoretical results are confirmed numerically, and it is shown that the error estimators can be used to design an optimally convergent adaptive scheme.

AB - In this paper, the discontinuous Petrov–Galerkin approximation of the Laplace eigenvalue problem is discussed. We consider in particular the primal and ultraweak formulations of the problem and prove the convergence together with a priori error estimates. Moreover, we propose two possible error estimators and perform the corresponding a posteriori error analysis. The theoretical results are confirmed numerically, and it is shown that the error estimators can be used to design an optimally convergent adaptive scheme.

UR - http://hdl.handle.net/10754/678294

UR - https://www.degruyter.com/document/doi/10.1515/cmam-2022-0069/html

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DO - 10.1515/cmam-2022-0069

M3 - Article

SN - 1609-4840

JO - Computational Methods in Applied Mathematics

JF - Computational Methods in Applied Mathematics

ER -

Discontinuous Petrov–Galerkin Approximation of Eigenvalue Problems

Abstract

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