# 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

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topBenbourhim, 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- 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
- 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.
- T. Iwaniec, C. Sbordone. Quasiharmonic fields. Ann. I. H. Poincaré-AN 18, 5 (2001), 519–572. Zbl1068.30011
- J. Peetre. Espaces d’interpolation et théorème de Soboleff. Ann. Inst. Fourier, Grenoble, 16 (1966), 279–317. Zbl0151.17903
- L. Schwartz. Théorie des distibutions. Hermann, Paris, 1966.
- E. Stein. Singular integrals and differentiability properties of functions. Princeton University Press, 1970. Zbl0207.13501

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