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

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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.

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Authors and Affiliations

  1. Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118, route de Narbonne, 31062, Toulouse Cedex 9, France

    Mohammed-Najib Benbourhim

  2. L.M.P.A, CNRS-FR2956, Université du Littoral Côte d’Opale, 50 rue F. Buisson, BP699, 62228, Calais Cedex, France

    Abderrahman Bouhamidi

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  1. Mohammed-Najib Benbourhim
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  2. Abderrahman Bouhamidi
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Correspondence to Abderrahman Bouhamidi.

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Benbourhim, MN., Bouhamidi, A. Pseudo-polyharmonic vectorial approximation for div-curl and elastic semi-norms. Numer. Math. 109, 333–364 (2008). https://doi.org/10.1007/s00211-008-0146-x

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  • DOI: https://doi.org/10.1007/s00211-008-0146-x

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