Meshless Polyharmonic Div-Curl Reconstruction

M. N. Benbourhim; A. Bouhamidi

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 7, page 55-59
  • ISSN: 0973-5348

Abstract

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In this paper, we will discuss the meshless polyharmonic reconstruction of vector fields from scattered data, possibly, contaminated by noise. We give an explicit solution of the problem. After some theoretical framework, we discuss some numerical aspect arising in the problems related to the reconstruction of vector fields

How to cite

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Benbourhim, M. N., and Bouhamidi, A.. Taik, A., ed. "Meshless Polyharmonic Div-Curl Reconstruction." Mathematical Modelling of Natural Phenomena 5.7 (2010): 55-59. <http://eudml.org/doc/197696>.

@article{Benbourhim2010,
abstract = {In this paper, we will discuss the meshless polyharmonic reconstruction of vector fields from scattered data, possibly, contaminated by noise. We give an explicit solution of the problem. After some theoretical framework, we discuss some numerical aspect arising in the problems related to the reconstruction of vector fields},
author = {Benbourhim, M. N., Bouhamidi, A.},
editor = {Taik, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {approximation theory; meshless approximation methods; radial basis functions; meshless approximation; curl-free; divergence-free; Helmholtz-Hodge decomposition},
language = {eng},
month = {8},
number = {7},
pages = {55-59},
publisher = {EDP Sciences},
title = {Meshless Polyharmonic Div-Curl Reconstruction},
url = {http://eudml.org/doc/197696},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Benbourhim, M. N.
AU - Bouhamidi, A.
AU - Taik, A.
TI - Meshless Polyharmonic Div-Curl Reconstruction
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/8//
PB - EDP Sciences
VL - 5
IS - 7
SP - 55
EP - 59
AB - In this paper, we will discuss the meshless polyharmonic reconstruction of vector fields from scattered data, possibly, contaminated by noise. We give an explicit solution of the problem. After some theoretical framework, we discuss some numerical aspect arising in the problems related to the reconstruction of vector fields
LA - eng
KW - approximation theory; meshless approximation methods; radial basis functions; meshless approximation; curl-free; divergence-free; Helmholtz-Hodge decomposition
UR - http://eudml.org/doc/197696
ER -

References

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  1. M. N. Benbourhim, A. Bouhamidi. Pseudo-polyharmonic vectorial approximation for div-curl and elastic semi-norms. Numer. Math., 109 (2008), No. 3, 333–364. 
  2. J. Duchon. Splines minimizing rotation-invariant seminorms in Sobolev spaces. In constructive theory of functions of several variables, eds. W. Schempp and K. Zeller, Lecture notes in mathematics, vol. 571, Springer-Verlag, Berlin, (1977), 85–100.  
  3. T. Iwaniec, C. Sbordone. Quasiharmonic fields. Ann. I. H. Poincaré-AN 18, 5 (2001), 519–572. 
  4. J. Peetre. Espaces d’interpolation et théorème de Soboleff. Ann. Inst. Fourier, Grenoble, 16 (1966), 279–317. 
  5. L. Schwartz. Théorie des distibutions. Hermann, Paris, 1966.  
  6. E. Stein. Singular integrals and differentiability properties of functions. Princeton University Press, 1970.  

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