Geodesic
Meshless Polyharmonic Div-Curl Reconstruction
M. N. Benbourhim1 ; A. Bouhamidi2
1 Institute of Mathematics of Toulouse, University of Paul Sabatier, 118, route de Narbonne, F-31062 Toulouse Cedex 9, France
2 University of Lille Nord de France, ULCO, L.M.P.A, 50, rue F. Buisson, BP 699,F-62228 Calais Cedex, France
Mathematical modelling of natural phenomena, Tome 5 (2010) no. 7 Supplement, pp. 55-59

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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
DOI : 10.1051/mmnp/20105709

M. N. Benbourhim 1 ; A. Bouhamidi 2

1 Institute of Mathematics of Toulouse, University of Paul Sabatier, 118, route de Narbonne, F-31062 Toulouse Cedex 9, France
2 University of Lille Nord de France, ULCO, L.M.P.A, 50, rue F. Buisson, BP 699,F-62228 Calais Cedex, France 
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M. N. Benbourhim; A. Bouhamidi. Meshless Polyharmonic Div-Curl Reconstruction. Mathematical modelling of natural phenomena, Tome 5 (2010) no. 7 Supplement, pp. 55-59. doi: 10.1051/mmnp/20105709

[1] M. N. Benbourhim, A. Bouhamidi Pseudo-polyharmonic vectorial approximation for div-curl and elastic semi-norms Numer. Math. 2008 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 2001 519 572

[4] J. Peetre Espaces d’interpolation et théorème de Soboleff Ann. Inst. Fourier, Grenoble 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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