A Residual a Posteriori Error Estimator for Elasto-Viscoplasticity

Abstract

The numerical approximation of an elasto-viscoplastic problem is considered in this paper. Fully discrete approximations are obtained by using the finite element method to approximate the spatial variable and the forward Euler scheme to discretize time derivatives. We first recall an a priori estimate result from which the linear convergence of the algorithm is derived under suitable regularity conditions. Then, an a posteriori error analysis is provided. Upper and lower error bounds are obtained.