MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.

Dec 10, 2000
Dec 10, 2000
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