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Plane wave approximation of homogeneous Helmholtz solutions

Moiola, A. ; Hiptmair, R. ; Perugia, I.

In: Zeitschrift für angewandte Mathematik und Physik, 2011, vol. 62, no. 5, p. 809-837

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    Title
    • Plane wave approximation of homogeneous Helmholtz solutions
    Author
    • Moiola, A.. SAM, ETH Zürich, 8092, Zürich, Switzerland
    • Hiptmair, R.. SAM, ETH Zürich, 8092, Zürich, Switzerland
    • Perugia, I.. Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100, Pavia, Italy
    Document Type
    • Postprint
    Language
    • English
    Published in
    • Zeitschrift für angewandte Mathematik und Physik, 2011, vol. 62, no. 5, p. 809-837. SP Birkhäuser Verlag Basel
    Other Version
    OAI-PMH Identifier
    • oai:doc.rero.ch:311946
    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