Numerical Analysis of a Relaxed Variational Model of Hysteresis in Two-Phase Solids
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)
2 Mathematical Institute, University of Warwick, Coventry, UK. (firstname.lastname@example.org)
Revised: 29 June 2001
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: 65N30 / 73C05
Key words: Variational problems / phase transitions / elasticity / hysteresis / a priori error estimates / a posteriori error estimates / adaptive algorithms / non-convex minimization / microstructure.
© EDP Sciences, SMAI, 2001