# A multiscale correction method for local singular perturbations of the boundary

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

- Volume: 41, Issue: 1, page 111-127
- ISSN: 0764-583X

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topDambrine, Marc, and Vial, Grégory. "A multiscale correction method for local singular perturbations of the boundary." ESAIM: Mathematical Modelling and Numerical Analysis 41.1 (2007): 111-127. <http://eudml.org/doc/250067>.

@article{Dambrine2007,

abstract = {
In this work, we consider singular perturbations of the boundary of a smooth domain. We describe the asymptotic behavior of the solution uE of a second order elliptic equation posed in the perturbed domain with respect to the size parameter ε of the deformation. We are also interested in the variations of the energy functional. We propose a numerical method for the approximation of uE based on a multiscale superposition of the unperturbed solution u0 and a profile defined in a model domain. We conclude with numerical results.
},

author = {Dambrine, Marc, Vial, Grégory},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Multiscale asymptotic analysis; shape optimization; patch of elements.; multiscale asymptotic analysis; patch of elements; Poisson equation; numerical examples; finite elements; asymptotic expansion; Laplace equation},

language = {eng},

month = {4},

number = {1},

pages = {111-127},

publisher = {EDP Sciences},

title = {A multiscale correction method for local singular perturbations of the boundary},

url = {http://eudml.org/doc/250067},

volume = {41},

year = {2007},

}

TY - JOUR

AU - Dambrine, Marc

AU - Vial, Grégory

TI - A multiscale correction method for local singular perturbations of the boundary

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2007/4//

PB - EDP Sciences

VL - 41

IS - 1

SP - 111

EP - 127

AB -
In this work, we consider singular perturbations of the boundary of a smooth domain. We describe the asymptotic behavior of the solution uE of a second order elliptic equation posed in the perturbed domain with respect to the size parameter ε of the deformation. We are also interested in the variations of the energy functional. We propose a numerical method for the approximation of uE based on a multiscale superposition of the unperturbed solution u0 and a profile defined in a model domain. We conclude with numerical results.

LA - eng

KW - Multiscale asymptotic analysis; shape optimization; patch of elements.; multiscale asymptotic analysis; patch of elements; Poisson equation; numerical examples; finite elements; asymptotic expansion; Laplace equation

UR - http://eudml.org/doc/250067

ER -

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