Error estimates in elastoplasticity using a mixed method

Andreas Schroeder ,Sebastian Wiedemann

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 16

MSC 2000

65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

65N15 Error bounds

Abstract
In this paper, a mixed formulation and its discretization are introduced for elastoplasticity with linear kinematic hardening. The mixed formulation relies on the introduction of a Lagrange multiplier to resolve the non-differentia\-bility of the plastic work function. The main focus is on the derivation of a~priori and a~posteriori error estimates based on general discretization spaces. The estimates are applied to several low-order finite elements. In particular, a~posteriori estimates are expressed in terms of standard residual estimates. Numerical experiments are presented, confirming the applicability of the a~posteriori estimates within an adaptive procedure.