# Linear convergence in the approximation of rank-one convex envelopes

- Volume: 38, Issue: 5, page 811-820
- ISSN: 0764-583X

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topBartels, Sören. "Linear convergence in the approximation of rank-one convex envelopes." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 38.5 (2004): 811-820. <http://eudml.org/doc/245551>.

@article{Bartels2004,

abstract = {A linearly convergent iterative algorithm that approximates the rank-1 convex envelope $f^\{rc\}$ of a given function $f:\mathbb \{R\}^\{n\times m\} \rightarrow \mathbb \{R\}$, i.e. the largest function below $f$ which is convex along all rank-1 lines, is established. The proposed algorithm is a modified version of an approximation scheme due to Dolzmann and Walkington.},

author = {Bartels, Sören},

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

keywords = {nonconvex variational problem; calculus of variations; relaxed variational problems; rank-1 convex envelope; microstructure; iterative algorithm; rank-one convex envelope; phase transitions; crystalline solids; algorithm; convergence; numerical experiments},

language = {eng},

number = {5},

pages = {811-820},

publisher = {EDP-Sciences},

title = {Linear convergence in the approximation of rank-one convex envelopes},

url = {http://eudml.org/doc/245551},

volume = {38},

year = {2004},

}

TY - JOUR

AU - Bartels, Sören

TI - Linear convergence in the approximation of rank-one convex envelopes

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2004

PB - EDP-Sciences

VL - 38

IS - 5

SP - 811

EP - 820

AB - A linearly convergent iterative algorithm that approximates the rank-1 convex envelope $f^{rc}$ of a given function $f:\mathbb {R}^{n\times m} \rightarrow \mathbb {R}$, i.e. the largest function below $f$ which is convex along all rank-1 lines, is established. The proposed algorithm is a modified version of an approximation scheme due to Dolzmann and Walkington.

LA - eng

KW - nonconvex variational problem; calculus of variations; relaxed variational problems; rank-1 convex envelope; microstructure; iterative algorithm; rank-one convex envelope; phase transitions; crystalline solids; algorithm; convergence; numerical experiments

UR - http://eudml.org/doc/245551

ER -

## References

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