Numerical analysis of a relaxed variational model of hysteresis in two-phase solids
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 5, p. 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
Keywords: variational problems, phase transitions, elasticity, hysteresis, a priori error estimates, a posteriori error estimates, adaptive algorithms, non-convex minimization, microstructure
@article{M2AN_2001__35_5_865_0,
     author = {Carstensen, Carsten and Plech\'a\v c, Petr},
     title = {Numerical analysis of a relaxed variational model of hysteresis in two-phase solids},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {5},
     year = {2001},
     pages = {865-878},
     zbl = {1007.74062},
     mrnumber = {1866271},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2001__35_5_865_0}
}
Carstensen, Carsten; Plecháč, Petr. Numerical analysis of a relaxed variational model of hysteresis in two-phase solids. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 5, pp. 865-878. http://www.numdam.org/item/M2AN_2001__35_5_865_0/

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