00-33   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Carsten Carstensen, Petr Plechac:

Numerical Analysis of a Relaxed Variational Model of Hysteresis in Two-Phase Solids

This paper presents the numerical analysis for a variational formulation of rate-independent phase transformations in elastic solids due to Mielke et al. The new model itself suggests an implicit time-discretization which is combined with the finite element method in space. A~priori error estimates are established for the quasioptimal spatial approximation of the stress field within one time-step. A posteriori error estimates motivate an adaptive mesh-refining algorithm for efficient discretization. The proposed scheme enables numerical simulations which show that the model allows for hysteresis.

Mathematics Subject Classification (1991): 65N30, 73C05

Keywords: variational problems, phase transitions, elasticity, hysteresis, a priori error estimates, a posteriori error estimates, adaptive algorithms, non-convex minimization, microstructure

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[Thu Feb 19 18:56:35 2009]
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