A multiscale correction method for local singular perturbations of the boundary

DOI10.1051/m2an:2007012zbMath1129.65084OpenAlexW2010129435MaRDI QIDQ3595160

Marc Dambrine, Grégory Vial

Publication date: 10 August 2007

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=M2AN_2007__41_1_111_0

zbMATH Keywords

finite elementsasymptotic expansionnumerical examplesLaplace equationshape optimizationPoisson equationmultiscale asymptotic analysispatch of elements

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (8)

A thick‐point approximation of a small body embedded in an elastic medium: justification with an asymptotic analysis ⋮ An \(L^p\) theory of linear elasticity in the half-space ⋮ Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers ⋮ On moderately close inclusions for the Laplace equation ⋮ Multi-scale asymptotic expansion for a small inclusion in elastic media ⋮ Augmented Galerkin schemes for the numerical solution of scattering by small obstacles ⋮ A numerical approach for the Poisson equation in a planar domain with a small inclusion ⋮ INTERACTIONS BETWEEN MODERATELY CLOSE INCLUSIONS FOR THE LAPLACE EQUATION

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Non-reflecting boundary conditions
• Matching and multiscale expansions for a model singular perturbation problem
• Asymptotic analysis of shape functionals
• The Localized Finite Element Method and Its Application to the Two-Dimensional Sea-Keeping Problem
• Absorbing Boundary Conditions for the Numerical Simulation of Waves
• Shape optimization by the homogenization method

This page was built for publication: A multiscale correction method for local singular perturbations of the boundary