Numerische Mathematik

, Volume 109, Issue 3, pp 333–364 | Cite as

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

  • Mohammed-Najib Benbourhim
  • Abderrahman Bouhamidi


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.

Mathematics Subject Classification (2000)

41A15 65D05 65D10 46F10 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Mohammed-Najib Benbourhim
    • 1
  • Abderrahman Bouhamidi
    • 2
  1. 1.Institut de Mathématiques de ToulouseUniversité Paul SabatierToulouse Cedex 9France
  2. 2.L.M.P.A, CNRS-FR2956Université du Littoral Côte d’OpaleCalais CedexFrance

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