Open AccessHigh order extended finite element method for cracked domains
Author(s) -
Pierre Laborde,
Julien Pommier,
Yves Renard,
Michel Salaün
Publication year - 2005
Publication title -
hal (le centre pour la communication scientifique directe)
Language(s) - English
DOI - 10.1002/nme.1370/abstract
Subject(s) - finite element method , order (exchange) , element (criminal law) , extended finite element method , structural engineering , computer science , mathematics , materials science , engineering , business , political science , finance , law
International audienceThe aim of the paper is to study the capabilities of the Extended Finite Element Method (XFEM) to achieve accurate computations in non smooth situations such as crack problems. Although the XFEM method ensures a weaker error than classical nite element methods, the rate of convergence is not improved when the mesh parameter h is going to zero because of the presence of a singularity. The diculty can be overcome by modifying the enrichment of the nite element basis with the asymptotic crack tip displacement solutions as well as with the Heaviside function. Numerical simulations show that the modied XFEM method achieves an optimal rate of convergence (i.e. like in a standard nite element method for a smooth problem