Enrichissement des interpolations d'elements finis en utilisant des méthodes de particules

Abstract

In the framework of meshless methods the interpolation is based on a distribution of particles : it is not necessary to define connectivities. In this 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 suffers 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.