On error estimator and p-adaptivity in the generalized finite element method
Article first published online: 11 JUN 2004
Copyright © 2004 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Engineering
Volume 60, Issue 14, pages 2373–2398, 14 August 2004
How to Cite
Barros, F. B., Proença, S. P. B. and de Barcellos, C. S. (2004), On error estimator and p-adaptivity in the generalized finite element method. Int. J. Numer. Meth. Engng., 60: 2373–2398. doi: 10.1002/nme.1048
- Issue published online: 12 JUL 2004
- Article first published online: 11 JUN 2004
- Manuscript Accepted: 24 OCT 2003
- Manuscript Revised: 3 JUL 2003
- Manuscript Received: 21 NOV 2002
- finite element method;
- meshless methods;
- error estimation
This paper addresses the issue of a p-adaptive version of the generalized finite element method (GFEM). The technique adopted here is the equilibrated element residual method, but presented under the GFEM approach, i.e., by taking into account the typical nodal enrichment scheme of the method. Such scheme consists of multiplying the partition of unity functions by a set of enrichment functions. These functions, in the case of the element residual method are monomials, and can be used to build the polynomial space, one degree higher than the one of the solution, in which the error functions is approximated. Global and local measures are defined and used as error estimator and indicators, respectively. The error indicators, calculated on the element patches that surrounds each node, are used to control a refinement procedure. Numerical examples in plane elasticity are presented, outlining in particular the effectivity index of the error estimator proposed. Finally, the -adaptive procedure is described and its good performance is illustrated by the last numerical example. Copyright © 2004 John Wiley & Sons, Ltd.