98-18   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Jochen Alberty, Carsten Carstensen:

Numerical Analysis of Time-depending Primal Elastoplasticity with Hardening

The quasi-static elastoplastic evolution problem with combined isotropic and kinematic hardening is considered with emphasis on optimal convergence of the lowest order scheme. In each time-step of a generalised mid-point scheme such as the implicit Euler or the Crank-Nicholson scheme, the spatial discretisation consists in minimising a convex but non-smooth function on a subspace of continuous piecewise linear resp. piecewise constant trial functions. An a priori error estimate is established for the fully-discrete method which, for smooth data and a smooth exact solution, proves linear convergence as the mesh-size tends to zero. Strong convergence of the time-derivatives is established under mild conditions on the mesh and time-step sizes. Numerical experiments confirm our theoretical predictions and indicate the superiority of the implicit Euler scheme over the Crank-Nicholson scheme in practise.

Mathematics Subject Classification (1991): 65N30, 65R20, 73C5

Bibliographical note: accepted for publication in SIAM J. Numer. Anal.

Keywords: elastoplasticity, variational inequalities, time-discretisation, a priori error estimates, plasticity with hardening, Jensen-inequality

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