INTERNATIONAL JOURNAL OF c © 2009 Institute for Scientific NUMERICAL ANALYSIS AND MODELING Computing and Information Volume 6, Number 4, Pages 603–614 A RESIDUAL A POSTERIORI ERROR ESTIMATOR FOR

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 approx-imate 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. Key words. Elasto-viscoplasticity, fully discrete approximations, a posteriori error estimates, finite elements. 1