# Multiscale expansion and numerical approximation for surface defects⋆

V. Bonnaillie-Noël; D. Brancherie; M. Dambrine; F. Hérau; S. Tordeux; G. Vial

ESAIM: Proceedings (2011)

- Volume: 33, page 22-35
- ISSN: 1270-900X

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topBonnaillie-Noël, V., et al. Dobrzynski, Cécile, Colin, Thierry, and Abgrall, Rémi, eds. "Multiscale expansion and numerical approximation for surface defects⋆." ESAIM: Proceedings 33 (2011): 22-35. <http://eudml.org/doc/251213>.

@article{Bonnaillie2011,

abstract = {This paper is a survey of articles [5, 6, 8, 9, 13, 17, 18]. We are interested in the influence of small geometrical perturbations on the solution of elliptic problems. The cases of a single inclusion or several well-separated inclusions have been deeply studied. We recall here techniques to construct an asymptotic expansion. Then we consider moderately close inclusions, i.e. the distance between the inclusions tends to zero more slowly than their characteristic size. We provide a complete asymptotic description of the solution of the Laplace equation. We also present numerical simulations based on the multiscale superposition method derived from the first order expansion (cf [9]). We give an application of theses techniques in linear elasticity to predict the behavior till rupture of materials with microdefects (cf [6]). We explain how some mathematical questions about the loss of coercivity arise from the computation of the profiles appearing in the expansion (cf [8]).},

author = {Bonnaillie-Noël, V., Brancherie, D., Dambrine, M., Hérau, F., Tordeux, S., Vial, G.},

editor = {Dobrzynski, Cécile, Colin, Thierry, Abgrall, Rémi},

journal = {ESAIM: Proceedings},

language = {eng},

month = {12},

pages = {22-35},

publisher = {EDP Sciences},

title = {Multiscale expansion and numerical approximation for surface defects⋆},

url = {http://eudml.org/doc/251213},

volume = {33},

year = {2011},

}

TY - JOUR

AU - Bonnaillie-Noël, V.

AU - Brancherie, D.

AU - Dambrine, M.

AU - Hérau, F.

AU - Tordeux, S.

AU - Vial, G.

AU - Dobrzynski, Cécile

AU - Colin, Thierry

AU - Abgrall, Rémi

TI - Multiscale expansion and numerical approximation for surface defects⋆

JO - ESAIM: Proceedings

DA - 2011/12//

PB - EDP Sciences

VL - 33

SP - 22

EP - 35

AB - This paper is a survey of articles [5, 6, 8, 9, 13, 17, 18]. We are interested in the influence of small geometrical perturbations on the solution of elliptic problems. The cases of a single inclusion or several well-separated inclusions have been deeply studied. We recall here techniques to construct an asymptotic expansion. Then we consider moderately close inclusions, i.e. the distance between the inclusions tends to zero more slowly than their characteristic size. We provide a complete asymptotic description of the solution of the Laplace equation. We also present numerical simulations based on the multiscale superposition method derived from the first order expansion (cf [9]). We give an application of theses techniques in linear elasticity to predict the behavior till rupture of materials with microdefects (cf [6]). We explain how some mathematical questions about the loss of coercivity arise from the computation of the profiles appearing in the expansion (cf [8]).

LA - eng

UR - http://eudml.org/doc/251213

ER -

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