A multiscale correction method for local singular perturbations of the boundary

Marc Dambrine; Grégory Vial

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

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

Abstract

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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.

How to cite

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Dambrine, 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 -

References

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