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A posteriori error estimation (indication) for extended finite element methods (XFEM)

Extended finite element methods (XFEM) have been employed in computational fracture mechanics contexts since their inception in 1999. Although some work has been performed, leading to the first adaptive strategies for the generalised finite element method (GFEM), little or no work has been published on error estimation and adaptive approximations for XFEM. A first attempt at this challenging problem is published here: 

A simple error estimator for extended finite elementsStéphane Bordas 1 *, Marc Duflot 2, Phong Le 3

The authors would like to take this opportunity to generate discussion on this topic on iMechanica, and would welcome any critiques on the work above. 

Thank you in advance, and best regards from Glasgow,

Stephane Bordas 

I am Ramin Aghababaei , new PhD student at Mechanical Department of National University of Singapore. My thesis is about finite element modelling of nanocomposites.  Because I am at the first way of my research, I want to know more about my research topic  and know exactly why I want to do  or what is the problem and how can I solve it?   So I have some questions and your experience is invaluable for me in this way. 1-what are the important parameters in the modelling of nanostructures which must be considered? 2-what is the main problem of current finite element method to model the nanostructure, especially nanocomposite materials(for example in traditional methods or in ABAQUS program)? 3-Can we expand traditional methods like as Rayleigh-Ritz or Least square methods to model and analysis of nanocomposites?   Thank you very much . Regards, Ramin


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