Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-10T14:46:08.581Z Has data issue: false hasContentIssue false
  • English
  • Français

Meshless Polyharmonic Div-Curl Reconstruction

Published online by Cambridge University Press:  26 August 2010

A. Taik ,
M. N. Benbourhim  and
A. Bouhamidi
M. N. Benbourhim
Affiliation:
Institute of Mathematics of Toulouse, University of Paul Sabatier, 118, route de Narbonne, F-31062 Toulouse Cedex 9, France
A. Bouhamidi*
Affiliation:
University of Lille Nord de France, ULCO, L.M.P.A, 50, rue F. Buisson, BP 699,F-62228 Calais Cedex, France
*
*Corresponding author: E-mail:a.bouhamidi@lmpa.univ-littoral.fr
Get access

Abstract

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

Keywords

approximation theorymeshless approximation methodsradial basis functions
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 7: JANO9 – The 9thInternational Conference on Numerical Analysis and Optimization , 2010 , pp. 55 - 59
Copyright
© EDP Sciences, 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Benbourhim, M. N., Bouhamidi, A.. Pseudo-polyharmonic vectorial approximation for div-curl and elastic semi-norms . Numer. Math., 109 (2008), No. 3, 333–364.CrossRefGoogle Scholar
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.
Iwaniec, T., Sbordone, C.. Quasiharmonic fields . Ann. I. H. Poincaré-AN 18, 5 (2001), 519–572.CrossRefGoogle Scholar
Peetre, J.. Espaces d’interpolation et théorème de Soboleff . Ann. Inst. Fourier, Grenoble, 16 (1966), 279–317.CrossRefGoogle Scholar
L. Schwartz. Théorie des distibutions. Hermann, Paris, 1966.
E. Stein. Singular integrals and differentiability properties of functions. Princeton University Press, 1970.