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MiS Preprint

Numerical analysis of a relaxed variational model of hysteresis in two-phase solids

Carsten Carstensen and Petr Plechac


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.

MSC Codes:
65N30, 73C05
variational problem, phase transitions, elasticity, hysteresis, a-priori error estimates, a-posteriori estimates, adaptive algorithms, non-convex minimization, microstructure

Related publications

2001 Repository Open Access
Carsten Carstensen and Petr Plechac

Numerical analysis of a relaxed variational model of hysteresis in two-phase solids

In: ESAIM / Mathematical modelling and numerical analysis, 35 (2001) 5, pp. 865-878