C. Carstensen et P. Plechac, Numerical analysis of a relaxed variational model of hysteresis in two-phase solids, ESAIM-M MOD, 35(5), 2001, pp. 865-878
Citations number
24
Categorie Soggetti
Mathematics
Journal title
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
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 fi
eld 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 hysteres
is.