Keywords: verification, error, quantities of interest, upper bound, plasticity.

In the mechanical field a major concern has always been to control the quality of finite element computations. Today, more than ever, modeling and simulation are central to any mechanical engineering activity. A constant concern both in industry and research has been the verification of the models, which, today, can achieve very high levels of complexity.

In the past, only the global estimate of the discretization error (energy-norm) were used. A state of the art can be found in [1,2]. Most of the time, such a global information is insufficient for dimensioning purposes in mechanical design. Indeed, in many common situations, the dimensioning criteria involve local values, for example stresses, displacements, intensity factors. Consequently, more recently the research focuses on the evaluation of the quality of local quantities of interest. Now, for linear problems, methods have been developed, and some of them lead to strict and sharp bounds, for global and local quantities [2].

The objective here is to obtain similar results for non-linear problems. Such an estimation upon quantity of interest remains a widely open investigation field in this framework.

However, a new error computation method leading to strict bounds has been proposed in [3,4]. Two main concepts are introduced: the mirror problem instead of the adjoint problem one, and the dissipation error. This paper is the first application to this method to plasticity, the goal being to get sharp strict bounds. So, the first elements of the finite element technology to handle the bounding method are developed.

1

I. Babuska, T. Strouboulis, "The finite element method and its reliability", Oxford university press, 2001.

2

P. Ladevèze, J.-P. Pelle, "Mastering calculations in linear and nonlinear mechanics", Springer NY, 2004.

3

P. Ladevèze, "Upper error bounds on calculated outputs of interest for linear and nonlinear structural problems", Compte Rendus Académie des sciences - Mécanique, Paris, 334:299-407, 2006.

4

P. Ladevèze, "Strict upper error bounds on calculated outputs of interest in computational structural mechanics", Computational Mechanics, 2007, available online.

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