Computational Mechanics

, Volume 10, Issue 5, pp 307–318 | Cite as

Generalizing the finite element method: Diffuse approximation and diffuse elements

  • B. Nayroles
  • G. Touzot
  • P. Villon


This paper describes the new “diffuse approximation” method, which may be presented as a generalization of the widely used “finite element approximation” method. It removes some of the limitations of the finite element approximation related to the regularity of approximated functions, and to mesh generation requirements. The diffuse approximation method may be used for generating smooth approximations of functions known at given sets of points and for accurately estimating their derivatives. It is useful as well for solving partial differential equations, leading to the so called “diffuse element method” (DEM), which presents several advantages compared to the “finite element method” (FEM), specially for evaluating the derivatives of the unknown functions.


Differential Equation Finite Element Method Partial Differential Equation Approximation Method Information Theory 
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  1. Nayroles, B.; Touzot, G.; Villon, P. (1991a): La méthode des éléments diffus. C.R. Acad. Sci. Paris, t. 313, Série II, pp 293–296Google Scholar
  2. Nayroles, B.; Touzot, G.; Villon, P. (1991b): L'approximation diffuse. C.R. Acad. Sci. Paris, t. 313, Série II, pp 133–138Google Scholar
  3. Nayroles, B.; Touzot, G.; Villon, P. (1991c): Nuages de Points et Approximation diffuse. Séminaire d'analyse convexe, Exposé no 16, Université de Montpellier IIGoogle Scholar
  4. Nayroles, B.; Touzot, G.: Using diffuse approximation for optimizing antisound sources location. (submitted to J.S.V.)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • B. Nayroles
    • 1
  • G. Touzot
    • 2
  • P. Villon
    • 3
  1. 1.Institut de Mécanique de GrenobleCNRS (UMR 101)-Université Joseph FourierGrenobleFrance
  2. 2.Université de Technologie de Compiègne-CNRS (D 6063)-Pôle de Modélisation PicardieCompiègneFrance
  3. 3.Université de Technologie de Compiègne-CNRS (URA 817)-Pôle de Modélisation PicardieCompiègneFrance

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