Approximation of PDE eigenvalue problems involving parameter dependent matrices

Daniele Boffi; Francesca Gardini; Lucia Gastaldi

doi:10.1007/s10092-020-00390-6

Approximation of PDE eigenvalue problems involving parameter dependent matrices

Daniele Boffi, Francesca Gardini, Lucia Gastaldi

King Abdullah University of Science and Technology

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

10 Scopus citations

Abstract

We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form Ax= λBx, where the matrices A and/or B may depend on a scalar parameter. Parameter dependent matrices occur frequently when stabilized formulations are used for the numerical approximation of partial differential equations. With the help of classical numerical examples we show that the presence of one (or both) parameters can produce unexpected results.

Original language	English (US)
Journal	Calcolo
Volume	57
Issue number	4
DOIs	https://doi.org/10.1007/s10092-020-00390-6
State	Published - Nov 11 2020

Bibliographical note

KAUST Repository Item: Exported on 2020-11-17
Acknowledgements: The authors are members of INdAM Research group GNCS and their research is supported by PRIN/MIUR. The research of the first and third authors is partially supported by IMATI/CNR.

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10.1007/s10092-020-00390-6

https://repository.kaust.edu.sa/bitstream/10754/665535/3/Boffi2020_Article_ApproximationOfPDEEigenvaluePr%20%281%29.pdf

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title = "Approximation of PDE eigenvalue problems involving parameter dependent matrices",

abstract = "We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form Ax= λBx, where the matrices A and/or B may depend on a scalar parameter. Parameter dependent matrices occur frequently when stabilized formulations are used for the numerical approximation of partial differential equations. With the help of classical numerical examples we show that the presence of one (or both) parameters can produce unexpected results.",

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AU - Gardini, Francesca

AU - Gastaldi, Lucia

N1 - KAUST Repository Item: Exported on 2020-11-17 Acknowledgements: The authors are members of INdAM Research group GNCS and their research is supported by PRIN/MIUR. The research of the first and third authors is partially supported by IMATI/CNR.

PY - 2020/11/11

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N2 - We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form Ax= λBx, where the matrices A and/or B may depend on a scalar parameter. Parameter dependent matrices occur frequently when stabilized formulations are used for the numerical approximation of partial differential equations. With the help of classical numerical examples we show that the presence of one (or both) parameters can produce unexpected results.

AB - We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form Ax= λBx, where the matrices A and/or B may depend on a scalar parameter. Parameter dependent matrices occur frequently when stabilized formulations are used for the numerical approximation of partial differential equations. With the help of classical numerical examples we show that the presence of one (or both) parameters can produce unexpected results.

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SN - 1126-5434

VL - 57

JO - Calcolo

JF - Calcolo

IS - 4

ER -

Approximation of PDE eigenvalue problems involving parameter dependent matrices

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