Hierarchical Model- and Discretization-error Estimation of Elasto-plastic Structures

Abstract

A posteriori error estimators of the discretization and model errors are presented for finite-element solutions of small-strain elasto-plasticity and large-strain elasticity problems. The described posterior equilibrium method (PEM) also yields anisotropic error indicators that are more efficient for thin-walled structures than isotropic ones. The model error in a sequence of hierarchical mathematical models and related dimensions can be as important as the discretization error. Therefore, integrated error-controlled adaptivity of finite-element approximations and of models in relevant subdomains, such as thickness jumps, is a challenging task for complex engineering structures. The posterior equilibrium method yields an effective estimation of discretization errors and model errors in general. Based on this approach, an upper bound of the error in a local quantity of interest can be obtained by solving an auxiliary local Neumann problem for the error of the dual problem. Some illustrative examples show the numerical and physical features of the methodologies.