98-13   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Jochen Alberty, Carsten Carstensen, Darius Zarrabi:

Adaptive numerical analysis in primal elastoplasticity with hardening

The quasi-static viscoplastic resp. elastoplastic evolution problem with isotropic or kinematic hardening is considered with emphasis on optimal convergence and adapted mesh-refining in the spatial discretization. Within one time-step of an implicit time-discretization, the finite element method leads to a minimisation problem for non-smooth convex functions on discrete subspaces. For piecewise constant resp. affine ansatz functions, the stress resp. displacement approximations are experimentally and theoretically shown to converge linearly. An a~posteriori error estimate then justifies an automatic adaptive mesh-refining algorithm. Numerical examples support the superiority of the adapted mesh.

Mathematics Subject Classification (1991): 65N30, 65R20, 73C50

Bibliographical note: Comput. Methods Appl. Engrg. 171 (1999) 175-204.

Keywords: elastoplasticity, plasticity with hardening, variational inequalities, a priori error estimates, a posteriori estimates, adaptive algorithms

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[Thu Feb 19 18:56:34 2009]
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