Plane wave approximation of homogeneous Helmholtz solutions
type: Item
instance of: scholarly article
title: Plane wave approximation of homogeneous Helmholtz solutions
zbMATH Open document ID: 1263.35070
author: Ralf Hiptmair
author: Andrea Moiola
author: Ilaria Perugia
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2013-02-04T00:00:00Z
full work available at URL: http://hdl.handle.net/20.500.11850/159705
review text: In this article, the approximation of solutions of homogeneous Helmholtz equations \(\Delta u+\omega^2u=0\) with constant coefficients and wave number \(\omega>0\) is considered using linear combinations of plane waves with different directions. The authors combine approximation estimates for homogeneous Helmholtz solutions by generalized harmonic polynomials that are obtained from Vekua's theory. They focus specifically on the estimates for the approximation of generalized harmonic polynomials by plane waves. In addition, best approximation error estimates in Sobolev norms are derived. Those are explicit in terms of the domain size, the number of plane waves, and the degree of the generalized polynomials.
reviewed by: Andreas Kleefeld
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A30
zbMATH DE Number: 6134359
zbMATH Keywords: approximation by plane waves
zbMATH Keywords: generalized harmonic polynomials
zbMATH Keywords: homogeneous Helmholtz solutions
zbMATH Keywords: Vekua's theory
zbMATH Keywords: Jacobi-Anger formula
MaRDI profile type: Publication
OpenAlex ID: W2010605025
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DOI: 10.1007/S00033-011-0147-Y
description: scientific article; zbMATH DE number 6134359