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

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

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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
Article number	41
Number of pages	21
Journal	CALCOLO
Volume	57
Issue number	4
DOIs	https://doi.org/10.1007/s10092-020-00390-6
Publication status	Published - Dec 2020
MoE publication type	A1 Journal article-refereed

Keywords

Eigenvalue problem
Parameter dependent matrices
Partial differential equations
Polygonal meshes
Virtual element method

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Boffi2020_Article_ApproximationOfPDEEigenvaluePrFinal published version, 3.1 MBLicence: CC BY

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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.

KW - Eigenvalue problem

KW - Parameter dependent matrices

KW - Partial differential equations

KW - Polygonal meshes

KW - Virtual element method

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Approximation of PDE eigenvalue problems involving parameter dependent matrices

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Keywords

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