Bounds for the \(N\) lowest eigenvalues of fourth-order boundary value problems
type: Item
instance of: scholarly article
title: Bounds for the \(N\) lowest eigenvalues of fourth-order boundary value problems
zbMATH Open document ID: 0883.65082
DOI: 10.1007/BF02684402
published in: Computing
publication date: 1997-09-04T00:00:00Z
review text: The author presents a method for calculating inclusion intervals to the first \(N\) (real) eigenvalues of certain fourth-order elliptic differential equations on bounded domains \(\Omega\) and under Dirichlet boundary conditions. The problem is treated in variational form in the Sobolev space \(H^2_0(\Omega)\), so that error bounds in terms of defects in the dual space \(H^{-2}(\Omega)\) may be introduced. In order to obtain a lower bound for the remainder of the spectrum, a boundary homotopy method is proposed. Impressing numerical results are presented for the 100 lowest eigenvalues of the clamped plate problem in the unit square, where rounding errors were controlled by interval analysis.
Mathematics Subject Classification ID: 65N25
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35J40
zbMATH DE Number: 1057395
zbMATH Keywords: inclusion intervals
zbMATH Keywords: eigenvalues
zbMATH Keywords: fourth-order elliptic differential equations
zbMATH Keywords: error bounds
zbMATH Keywords: boundary homotopy method
zbMATH Keywords: numerical results
zbMATH Keywords: clamped plate problem
zbMATH Keywords: interval analysis
author: Christian Wieners
reviewed by: Waldemar Velte
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1057395