Plane wave approximation of homogeneous Helmholtz solutions

Moiola, A., Hiptmair, R. and Perugia, I. (2011) Plane wave approximation of homogeneous Helmholtz solutions. Zeitschrift für angewandte Mathematik und Physik, 62 (5). pp. 809-837. ISSN 0044-2275 doi: 10.1007/s00033-011-0147-y

Abstract/Summary

In this paper, we study the approximation of solutions of the homogeneous Helmholtz equation Δu + ω 2 u = 0 by linear combinations of plane waves with different directions. We combine approximation estimates for homogeneous Helmholtz solutions by generalized harmonic polynomials, obtained from Vekua’s theory, with estimates for the approximation of generalized harmonic polynomials by plane waves. The latter is the focus of this paper. We establish best approximation error estimates in Sobolev norms, which are explicit in terms of the degree of the generalized polynomial to be approximated, the domain size, and the number of plane waves used in the approximations.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/28023
Identification Number/DOI	10.1007/s00033-011-0147-y
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Springer
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