Recovery based error estimation and adaptivity applied to a modified element-free Galerkin method

Abstract

In this work, we propose an error estimator of the recovery type, which considers the equilibrium and boundary traction conditions, and an h-refinement procedure that is applied to the modified element-free Galerkin (MEFG) method. The approximate solution obtained by the MEFG method satisfies accurately the essential boundary condition. However, the approximate MEFG stress field presents some discontinuities on a neighborhood of the essential boundary condition and may present some spurious oscillations at regions of high stress gradients or discontinuities. Thus, the h-adaptive scheme is responsible for the reduction not only of the global error but also of the local errors associated with the discontinuities and oscillations of the approximate stress field. In order to validate the proposed procedures, we present some numerical solution for some simple problems and consider the analysis of a complex component.

A model for the simulation of powder compaction processes

“…Here, one considers s = 1.5, what assures a covering of the entire domain. Moreover, the selection of the "optimal" value for s was based on the results derived in a parametric analysis, see Rossi and Alves [13,14]. An example of covering is presented in Fig.…”

A total Lagrangian framework for simulation of powder compaction process based on a smooth three‐surface Cap model and a mesh‐free method

“…Here, the optimal value of s = 1.5 was determined from a parametric analysis performed in References [40,41]. An example of the covering of a given domain is illustrated in Figure 6.…”

On the Analysis of an EFG Method Under Large Deformations and Volumetric Locking

“…Here, one considers s=1.5, what assures a covering of the entire domain. The selection of the proper parameter s, which characterizes the support size, was based on the results of a parametric analysis performed in Rossi and Alves [24,25]. Now, since the global shape functions I (X), I = 1, .…”