Numerical analysis of a relaxed variational model of hysteresis in two-phase solids
ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 5, pp. 865-878.

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.

Classification : 65N30, 73C05
Mots clés : variational problems, phase transitions, elasticity, hysteresis, a priori error estimates, a posteriori error estimates, adaptive algorithms, non-convex minimization, microstructure
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     title = {Numerical analysis of a relaxed variational model of hysteresis in two-phase solids},
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Carstensen, Carsten; Plecháč, Petr. Numerical analysis of a relaxed variational model of hysteresis in two-phase solids. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 5, pp. 865-878. http://www.numdam.org/item/M2AN_2001__35_5_865_0/

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