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

Published online by Cambridge University Press:  15 April 2002

Carsten Carstensen  and
Petr Plecháč
Carsten Carstensen
Affiliation:
Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Wiedner Hauptstraße 8-10/115, A-1040 Wien, Austria. (Carsten.Carstensen@tuwien.ac.at)
Petr Plecháč
Affiliation:
Mathematical Institute, University of Warwick, Coventry, UK. (plechac@maths.warwick.ac.uk)
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Abstract

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.

Keywords

Variational problemsphase transitionselasticityhysteresisa priori error estimatesa posteriori error estimatesadaptive algorithmsnon-convex minimizationmicrostructure.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 5 , September 2001 , pp. 865 - 878
Copyright
© EDP Sciences, SMAI, 2001

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