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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- 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 38.5 (2010): 811-820. <http://eudml.org/doc/194241>.

@article{Bartels2010,

abstract = {
A linearly convergent iterative algorithm that approximates the
rank-1 convex envelope $f^\{rc\}$ of a given function $f:\mathbb\{R\}^\{n\times m\} \to \mathbb\{R\}$,
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},

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

language = {eng},

month = {3},

number = {5},

pages = {811-820},

publisher = {EDP Sciences},

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

url = {http://eudml.org/doc/194241},

volume = {38},

year = {2010},

}

TY - JOUR

AU - Bartels, Sören

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

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

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 $f:\mathbb{R}^{n\times m} \to \mathbb{R}$,
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.; nonconvex variational problem; rank-one convex envelope; phase transitions; crystalline solids; algorithm; convergence; numerical experiments

UR - http://eudml.org/doc/194241

ER -

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