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

top
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

top

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

top
  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. Zbl1151.65325
  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. Zbl1068.30011
  4. J. Peetre. Espaces d’interpolation et théorème de Soboleff. Ann. Inst. Fourier, Grenoble, 16 (1966), 279–317. Zbl0151.17903
  5. L. Schwartz. Théorie des distibutions. Hermann, Paris, 1966.  
  6. E. Stein. Singular integrals and differentiability properties of functions. Princeton University Press, 1970.  Zbl0207.13501

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.