NUMERICAL ASSESSMENT OF A STRESS RECOVERY PROCEDURE APPLIED TO STABLE GFEM USING FLAT-TOP PARTITION OF UNITY

Resumo

The Generalized Finite Element Method (GFEM) is a Galerkin method based on augmenting
low-order FE approximation spaces with functions that well represent local behaviors of the solution.
Since its proposition, the method has demonstrated good performance and has provided higher-order
convergence rates. A particular drawback related to it, however, is the possibility of linear dependencies
between its shape functions, which leads to loss of accuracy and convergence rates decrease. In this
context, stable versions for the method, with modifications in the enrichment functions and Partitions of

Unity (PU), were developed aiming to eliminate these dependencies and keep GFEM optimal conver-
gence rates. On the other hand, it is known that for displacement formulations the stress field coming

from numerical approaches is less accurate than the main displacement field. Very recently, a stress
recovery procedure was proposed for Stable GFEM (SGFEM). This process is based on a weighted L
2
inner product, which leads to a block-diagonal matrix, being therefore very efficient. In this work, we
aim to assess this recovery procedure when applied to SGFEM using Flat-Top PU for quadrilateral FE
meshes. In particular, we evaluate the effect of using Lagrangian PU for weighting the L
2
inner product

used to generate the recovered stress field and the conditioning of this system coefficient matrix. Numer-
ical examples show that the combination of this GFEM version and the recovery procedure in addition

to guaranteeing stability for the solution also provides very accurate stress distributions.