# Numerical analysis of a relaxed variational model of hysteresis in two-phase solids

Carsten Carstensen; Petr Plecháč

- Volume: 35, Issue: 5, page 865-878
- ISSN: 0764-583X

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topCarstensen, Carsten, and 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 35.5 (2001): 865-878. <http://eudml.org/doc/194077>.

@article{Carstensen2001,

abstract = {$\!$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.},

author = {Carstensen, Carsten, Plecháč, Petr},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {variational problems; phase transitions; elasticity; hysteresis; a priori error estimates; a posteriori error estimates; adaptive algorithms; non-convex minimization; microstructure; variational formulation; two-phase solids; elastic solids; rate-independent phase transformations; implicit time discretization; quasioptimal spatial approximation of stress field; finite element method; adaptive mesh-refining algorithm},

language = {eng},

number = {5},

pages = {865-878},

publisher = {EDP-Sciences},

title = {Numerical analysis of a relaxed variational model of hysteresis in two-phase solids},

url = {http://eudml.org/doc/194077},

volume = {35},

year = {2001},

}

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 - Modélisation Mathématique et Analyse Numérique

PY - 2001

PB - EDP-Sciences

VL - 35

IS - 5

SP - 865

EP - 878

AB - $\!$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.

LA - eng

KW - variational problems; phase transitions; elasticity; hysteresis; a priori error estimates; a posteriori error estimates; adaptive algorithms; non-convex minimization; microstructure; variational formulation; two-phase solids; elastic solids; rate-independent phase transformations; implicit time discretization; quasioptimal spatial approximation of stress field; finite element method; adaptive mesh-refining algorithm

UR - http://eudml.org/doc/194077

ER -

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