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.
Mots-clés : 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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {865--878},
publisher = {EDP-Sciences},
volume = {35},
number = {5},
year = {2001},
mrnumber = {1866271},
zbl = {1007.74062},
language = {en},
url = {http://www.numdam.org/item/M2AN_2001__35_5_865_0/}
}
TY - JOUR AU - Carstensen, Carsten AU - Plecháč, Petr TI - Numerical analysis of a relaxed variational model of hysteresis in two-phase solids JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2001 SP - 865 EP - 878 VL - 35 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/item/M2AN_2001__35_5_865_0/ LA - en ID - M2AN_2001__35_5_865_0 ER -
%0 Journal Article %A Carstensen, Carsten %A Plecháč, Petr %T Numerical analysis of a relaxed variational model of hysteresis in two-phase solids %J ESAIM: Modélisation mathématique et analyse numérique %D 2001 %P 865-878 %V 35 %N 5 %I EDP-Sciences %U http://www.numdam.org/item/M2AN_2001__35_5_865_0/ %G en %F M2AN_2001__35_5_865_0
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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