# Numerical Analysis of a Relaxed Variational Model of Hysteresis in Two-Phase Solids

Carsten Carstensen; Petr Plecháč

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- 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 35.5 (2010): 865-878. <http://eudml.org/doc/197540>.

@article{Carstensen2010,

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},

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; hysteresis; rate-independent phase transformations; a posteriori error estimates; implicit time discretization; microstructure; quasioptimal spatial approximation of stress field; finite element method; a priori error estimates; adaptive mesh-refining algorithm},

language = {eng},

month = {3},

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/197540},

volume = {35},

year = {2010},

}

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

DA - 2010/3//

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; hysteresis; rate-independent phase transformations; a posteriori error estimates; implicit time discretization; microstructure; quasioptimal spatial approximation of stress field; finite element method; a priori error estimates; adaptive mesh-refining algorithm

UR - http://eudml.org/doc/197540

ER -

## References

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