Open AccessSpider XFEM, an extended finite element variant for partially unknown crack-tip displacement
Author(s) -
Elie Chahine,
Pierre Laborde,
Yves Renard
Publication year - 2008
Publication title -
european journal of computational mechanics
Language(s) - English
Resource type - Journals
eISSN - 2642-2085
pISSN - 2642-2050
DOI - 10.13052/remn.17.625-636
Subject(s) - extended finite element method , displacement (psychology) , finite element method , discretization , mathematics , convergence (economics) , a priori and a posteriori , rate of convergence , mathematical analysis , structural engineering , computer science , engineering , psychology , computer network , philosophy , channel (broadcasting) , epistemology , economics , psychotherapist , economic growth
In this paper, we introduce a new variant of the extended finite element method (Xfem) allowing an optimal convergence rate when the asymptotic displacement is partially unknown at the crack tip. This variant consists in the addition of an adapted discretization of the asymptotic displacement. We give a mathematical result of quasi-optimal a priori error estimate which allows to analyze the potentialities of the method. Some computational tests are provided and a comparison is made with the classical Xfem.