Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity

TL;DR

This paper introduces an improved error estimation method for the smoothed finite element method in linear elasticity, enhancing accuracy assessment during simulations, especially for singular problems.

Contribution

It proposes a recovery-based error estimator that enforces local equilibrium and decomposes stress for singular problems, improving error estimation accuracy.

Findings

Enhanced error estimates with better effectivity indices.

Effective for both smooth and singular elasticity problems.

Improves local and global error assessment accuracy.

Abstract

An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages compared to conventional finite element approximations. In particular, a widely cited strength of such methods is improved accuracy for the same computational cost. Yet, few attempts have been made to directly assess the quality of the results obtained during the simulation by evaluating an estimate of the discretization error. Here we propose a recovery type error estimator based on an enhanced recovery technique. The salient features of the recovery are: enforcement of local equilibrium and, for singular problems a "smooth+singular" decomposition of the recovered stress. We evaluate the proposed estimator on a number of test cases from linear elastic structural mechanics and obtain precise error estimations whose effectivities, both at local and global levels, are improved compared to recovery procedures not implementing these features.