A linearly convergent iterative algorithm that approximates the rank-1 convex envelope of a given function , i.e. the largest function below 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.
Mots clés : nonconvex variational problem, calculus of variations, relaxed variational problems, rank-1 convex envelope, microstructure, iterative algorithm
@article{M2AN_2004__38_5_811_0, author = {Bartels, S\"oren}, title = {Linear convergence in the approximation of rank-one convex envelopes}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {811--820}, publisher = {EDP-Sciences}, volume = {38}, number = {5}, year = {2004}, doi = {10.1051/m2an:2004040}, mrnumber = {2104430}, zbl = {1083.65058}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2004040/} }
TY - JOUR AU - Bartels, Sören TI - Linear convergence in the approximation of rank-one convex envelopes JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2004 SP - 811 EP - 820 VL - 38 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2004040/ DO - 10.1051/m2an:2004040 LA - en ID - M2AN_2004__38_5_811_0 ER -
%0 Journal Article %A Bartels, Sören %T Linear convergence in the approximation of rank-one convex envelopes %J ESAIM: Modélisation mathématique et analyse numérique %D 2004 %P 811-820 %V 38 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2004040/ %R 10.1051/m2an:2004040 %G en %F M2AN_2004__38_5_811_0
Bartels, Sören. Linear convergence in the approximation of rank-one convex envelopes. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 5, pp. 811-820. doi : 10.1051/m2an:2004040. http://www.numdam.org/articles/10.1051/m2an:2004040/
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