Enrichissement des interpolations d’éléments finis en utilisant des méthodes de particules

Author (s): Huerta, A., Fernández-Méndez, S. and Díez, P.
Journal: Mathematical Modelling and Numerical Analysis

Volume: 36, Issue 6
Pages: 1027 – 1042
Date: 2002

In the framework of meshless methods, the interpolation is based on a distribution of particles: it is not necessary to define connectivities. In these methods the interpolation can be easily enriched, increasing the number of particles (as in
h-refinement of finite elements) or increasing the order of consistency (as in p-refinement of finite elements). However, comparing with finite elements, particle methods suffer from an increase in the computational cost, mainly due to the computation of the shape functions. In this paper, a mixed interpolation that combines finite elements and particles is presented. The objective is to take advantage of both methods. In order to define h- p refinement strategies an a priori error estimate is needed, and thus, some convergence results are presented and proved for this mixed interpolation.(in French)



@article{ 2002-MMNA-HFD,
	author = {{Huerta, A.,Fern\'andez-M\'endez, S. and D\'iez, P.},
	title = {Enrichissement des interpolations d'éléments finis  en utilisant des méthodes sans
	journal = {ESAIM: M2AN},
	volume = 36,
	number = 6,
	pages = "1027-1042",
	year = 2002,
	DOI= "10.1051/m2an:2003004",
	url= "http://dx.doi.org/10.1051/m2an:2003004",