A simplified mode-based error estimation for plane stress/strain problems

The recently developed mode-based posteriori error estimation (Jung et al. 2022) exhibits excellent predictive capability as an error estimator. However, since its implementation requires trained network through deep learning, we focus on a simple mode-based error estimator for general use, without the network. In this paper, we propose a new posteriori error estimation using the simplified mode-based finite element formulation for the analysis of plane stress and plane strain problems. The proposed posteriori error estimation simply predicts an error calculated by the difference between the direct and recovered solutions of finite element analysis (FEA). To simply calculate the accurate recovered solution, geometry dependent bending modes and volumetric locking treatment are adopted. We demonstrate the predictive performance of the proposed error estimator through various numerical examples with 4-node finite elements.