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Parametric enrichment adaptivity by the extended finite element method
Author(s) -
Waisman Haim,
Belytschko Ted
Publication year - 2007
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2137
Subject(s) - finite element method , extended finite element method , parametric statistics , function (biology) , residual , boundary (topology) , mathematics , gravitational singularity , method of mean weighted residuals , boundary value problem , polynomial , parametric equation , mathematical optimization , mixed finite element method , computer science , algorithm , mathematical analysis , geometry , galerkin method , structural engineering , engineering , statistics , evolutionary biology , biology
An adaptive method within the extended finite element method (XFEM) framework which adapts the enrichment function locally to the physics of a problem, as opposed to polynomial or mesh refinement, is presented. The method minimizes a local residual and determines the parameters of the enrichment function. We consider an energy form and a ‘strong’ form of the residual as error measures to drive the algorithm. Numerical examples for boundary layers and solid mechanics problems illustrate that the procedure converges. Moreover, when only the character of the solution is known, a good approximation is obtained in the area of interest. It is also shown that the method can be used to determine the order of singularities in solutions. Copyright © 2007 John Wiley & Sons, Ltd.