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  1. Zeitschrift für angewandte Mathematik und Physik
  2. Zeitschrift für angewandte Mathematik und Physik : Volume 62
  3. Zeitschrift für angewandte Mathematik und Physik : Volume 62, Issue 5, October 2011
  4. Plane wave approximation of homogeneous Helmholtz solutions
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Zeitschrift für angewandte Mathematik und Physik : Volume 67
Zeitschrift für angewandte Mathematik und Physik : Volume 66
Zeitschrift für angewandte Mathematik und Physik : Volume 65
Zeitschrift für angewandte Mathematik und Physik : Volume 64
Zeitschrift für angewandte Mathematik und Physik : Volume 63
Zeitschrift für angewandte Mathematik und Physik : Volume 62
Zeitschrift für angewandte Mathematik und Physik : Volume 62, Issue 6, December 2011
Zeitschrift für angewandte Mathematik und Physik : Volume 62, Issue 5, October 2011
Polynomial, rational and analytic first integrals for a family of 3-dimensional Lotka-Volterra systems
Vekua theory for the Helmholtz operator
Plane wave approximation of homogeneous Helmholtz solutions
Exact soliton solutions of a D-dimensional nonlinear Schrödinger equation with damping and diffusive terms
Mathematical study of the small oscillations of a pendulum containing an almost homogeneous, incompressible, inviscid liquid and a barotropic gas (Oscillations of a pendulum with almost homogeneous liquid and gas)
Multiplicity and concentration of positive solutions for the Schrödinger–Poisson equations
Vortices in the three-dimensional thin-film Ginzburg–Landau model of superconductivity
Study of weak solutions for a fourth-order parabolic equation with variable exponent of nonlinearity
Propagation of a plane wave to a materially uniform but inhomogeneous body
Fractional order heat conduction law in magneto-thermoelasticity involving two temperatures
Radiation effects on the MHD flow near the stagnation point of a stretching sheet: revisited
Author’s response to Dr. Wadee and Yiatros’ discussion of my paper: “On interactive buckling in a sandwich structure” (ZAMP, vol. 61, pp. 565–577, 2010)
Zeitschrift für angewandte Mathematik und Physik : Volume 62, Issue 4, August 2011
Zeitschrift für angewandte Mathematik und Physik : Volume 62, Issue 3, June 2011
Zeitschrift für angewandte Mathematik und Physik : Volume 62, Issue 2, April 2011
Zeitschrift für angewandte Mathematik und Physik : Volume 62, Issue 1, February 2011
Zeitschrift für angewandte Mathematik und Physik : Volume 61
Zeitschrift für angewandte Mathematik und Physik : Volume 60
Zeitschrift für angewandte Mathematik und Physik : Volume 59
Zeitschrift für angewandte Mathematik und Physik : Volume 58
Zeitschrift für angewandte Mathematik und Physik : Volume 57
Zeitschrift für angewandte Mathematik und Physik : Volume 56
Zeitschrift für angewandte Mathematik und Physik : Volume 55
Zeitschrift für angewandte Mathematik und Physik : Volume 54
Zeitschrift für angewandte Mathematik und Physik : Volume 53
Zeitschrift für angewandte Mathematik und Physik : Volume 52
Zeitschrift für angewandte Mathematik und Physik : Volume 51
Zeitschrift für angewandte Mathematik und Physik : Volume 50
Zeitschrift für angewandte Mathematik und Physik : Volume 49
Zeitschrift für angewandte Mathematik und Physik : Volume 48

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Plane wave approximation of homogeneous Helmholtz solutions

Content Provider SpringerLink
Author Moiola, A. Hiptmair, R. Perugia, I.
Copyright Year 2011
Abstract 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.
Ending Page 837
Page Count 29
Starting Page 809
File Format PDF
ISSN 00442275
e-ISSN 14209039
Journal Zeitschrift für angewandte Mathematik und Physik
Issue Number 5
Volume Number 62
Language English
Publisher SP Birkhäuser Verlag Basel
Publisher Date 2011-07-12
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Approximation by plane waves Mathematical Methods in Physics Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation Vekua’s theory Approximation by other special function classes Homogeneous Helmholtz solutions Jacobi–Anger formula Theoretical and Applied Mechanics Generalized harmonic polynomials Rate of convergence, degree of approximation
Content Type Text
Resource Type Article
Subject Applied Mathematics Physics and Astronomy
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