Journal ArticleDOI
Spectral boundary homogenization in domains with oscillating boundaries
TLDR
In this article, the authors study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with a rapidly oscillating boundary.Abstract:
We study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with a rapidly oscillating boundary. We consider both cases where the eigenvalues of the limit problem are simple and multiple. We construct the leading terms of the asymptotic expansions for the eigenelements and verify the asymptotics.read more
Citations
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Journal ArticleDOI
Homogenization of Boundary Value Problems in Two-Level Thick Junctions Consisting of Thin Disks with Rounded or Sharp Edges
T. A. Mel’nik,D. Yu. Sadovyi +1 more
TL;DR: In this article, the authors considered a linear elliptic boundary value problem in a two-level thick junction of type 3 : 2 : 2 which consists of a cylinder with e-periodically stringed thin disks.
Journal ArticleDOI
Convergence Rates in Homogenization of the Mixed Boundary Value Problems
TL;DR: In this article, the convergence rates of solutions for homogenization of mixed boundary value problems were studied and the authors established the sharp rate of convergence in and, with no smoothness assumption on the coefficients.
References
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Book
Matching of asymptotic expansions of solutions of boundary value problems
A. M. Ilʹin,Viktor Minachin +1 more
Journal ArticleDOI
On the Roughness-Induced Effective Boundary Conditions for an Incompressible Viscous Flow
Willi Jäger,Andro Mikelić +1 more
TL;DR: In this article, the Navier friction condition was obtained for the laminar viscous channel flow with the lateral surface of the channel containing surface irregularities and the coefficient in the law was determined through an auxiliary boundary-layer type problem, and the tangential drag force and the effective mass flow were determined up to order O(e3/2).
Journal ArticleDOI
Effective Boundary Conditions for Laminar Flows over Periodic Rough Boundaries
TL;DR: In this paper, effective boundary conditions or wall laws are proposed for a laminar flow over a rough wall with periodic roughness elements, which allows the details of the wall to be avoided and dramatically reduces the computational cost.
Journal ArticleDOI
The Boundary-value Problem in Domains with Very Rapidly Oscillating Boundary☆
TL;DR: In this article, the authors studied the asymptotic behavior of the solution to boundary-value problem for the second order elliptic equation in the bounded domain with a very rapidly oscillating locally periodic boundary and showed that the limiting problem can involve Dirichlet, Fourier or Neumann boundary conditions depending on the structure of the coefficient of the original problem.