Geodesic
Numerical analysis of a relaxed variational model of hysteresis in two-phase solids
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 5, pp. 865-878

Voir la notice de l'article provenant de la source Numdam

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 },
     pages = {865--878},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {5},
     year = {2001},
     mrnumber = {1866271},
     zbl = {1007.74062},
     language = {en},
     url = {http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis 
PY  - 2001
SP  - 865
EP  - 878
VL  - 35
IS  - 5
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis 
%D 2001
%P 865-878
%V 35
%N 5
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 5, pp. 865-878. http://geodesic.mathdoc.fr/item/M2AN_2001__35_5_865_0/