Selections of shape functions for dimensional reduction to Helmholtz's equation

Kang Man Liu, Ivo Babuška

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The boundary value problem of Helmholtz's equation on a n + 1 dimensional thin slab is approximated by appropriate systems of the n-dimensional boundary value problem. The very detailed estimates for modeling error in the H1-norm demonstrate convergence when the thickness of the slab approaches 0 as well as when the size of the systems approaches infinity. Shape functions through the thickness are first selected by finitely many eigenfunctions, and the tail is then selected to consist of polynomials. The presence of two types of functions gives rise to a certain choice in the selection of a particular set of shape functions. Numerical results provide a good illustration of the effect of different choices for specific problems.

Original languageEnglish
Pages (from-to)169-190
Number of pages22
JournalNumerical Methods for Partial Differential Equations
Volume15
Issue number2
DOIs
Publication statusPublished - 1999 Mar

Fingerprint

Helmholtz equation
Dimensional Reduction
Shape Function
Helmholtz Equation
Boundary Value Problem
Boundary value problems
Modeling Error
Eigenfunctions
n-dimensional
Tail
Infinity
Norm
Eigenvalues and eigenfunctions
Numerical Results
Polynomial
Polynomials
Estimate
Demonstrate

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

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Selections of shape functions for dimensional reduction to Helmholtz's equation. / Liu, Kang Man; Babuška, Ivo.

In: Numerical Methods for Partial Differential Equations, Vol. 15, No. 2, 03.1999, p. 169-190.

Research output: Contribution to journalArticle

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