Pseudo-polyharmonic vectorial approximation for div-curl and elastic semi-norms

Authors:
Mohammed-Najib Benbourhim;Abderrahman Bouhamidi
Affiliations:
Université Paul Sabatier, Institut de Mathématiques de Toulouse, 118, route de Narbonne, 31062, Toulouse Cedex 9, France;Université du Littoral Côte d’Opale, L.M.P.A, CNRS-FR2956, BP699, 50 rue F. Buisson, 62228, Calais Cedex, France
Venue:
Numerische Mathematik
Year:
2008

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Abstract

Vector field reconstruction is a problem arising in many scientific applications. In this paper, we study a div-curl approximation of vector fields by pseudo-polyharmonic splines. This leads to the variational smoothing and interpolating spline problems with minimization of an energy involving the curl and the divergence of the vector field. The relationship between the div-curl energy and elastic energy is established. Some examples are given to illustrate the effectiveness of our approach for a vector field reconstruction.