Boundary layer tails in periodic homogenization

This paper focus on the properties of boundary layers in periodic homogenization in rectangular domains which are either fixed or have an oscillating boundary. Such boundary layers are highly oscillating near the boundary and decay exponentially fast in the interior to a non-zero limit that we call boundary layer tail. The influence of these boundary layer tails on interior error estimates is emphasized. They mainly have two effects (at first order with respect to the period e): first, they add a dispersive term to the homogenized equation, and second, they yield an effective Fourier boundary condition.

[1]  O. Pironneau,et al.  Domain decomposition and wall laws , 1995 .

[2]  M. Avellaneda,et al.  Compactness methods in the theory of homogenization , 1987 .

[3]  Willi Jäger,et al.  On the boundary conditions at the contact interface between a porous medium and a free fluid , 1996 .

[4]  Grégoire Allaire,et al.  Boundary layers in the homogenization of a spectral problem in fluid-solid structures , 1998 .

[5]  Robert V. Kohn,et al.  Reinforcement by a thin layer with oscillating thickness , 1987 .

[6]  Marco Avellaneda,et al.  Homogenization of elliptic problems withLp boundary data , 1987 .

[7]  A. Bensoussan,et al.  Asymptotic analysis for periodic structures , 1979 .

[8]  Grégoire Allaire,et al.  HOMOGENIZATION OF THE CRITICALITY SPECTRAL EQUATION IN NEUTRON TRANSPORT , 1999 .

[9]  Fadil Santosa,et al.  A dispersive effective medium for wave propagation in periodic composites , 1991 .

[10]  A. Bensoussan,et al.  Boundary Layers and Homogenization of Transport Processes , 1979 .

[11]  Habib Ammari,et al.  Diffraction at a Curved Grating: TM and TE Cases, Homogenization , 1996 .

[12]  Michael Vogelius,et al.  First-Order Corrections to the Homogenized Eigenvalues of a Periodic Composite Medium , 1993, SIAM J. Appl. Math..

[13]  E. Sanchez-Palencia.  Non-Homogeneous Media and Vibration Theory , 1980 .

[14]  Avner Friedman,et al.  The Boundary-value Problem in Domains with Very Rapidly Oscillating Boundary☆ , 1999 .

[15]  A. Bourgeat,et al.  NONLINEAR EFFECTS FOR FLOW IN PERIODICALLY CONSTRICTED CHANNEL CAUSED BY HIGH INJECTION RATE , 1998 .

[16]  G. Bal.  First-order corrector for the homogenization of the criticality eigenvalue problem in the even parity formulation of the neutron transport , 1999 .

[17]  Avner Friedman,et al.  A boundary value problem for the poisson equation with multi-scale oscillating Boundary , 1997 .

[18]  S. Moskow,et al.  First-order corrections to the homogenised eigenvalues of a periodic composite medium. A convergence proof , 1997, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[19]  Jacques-Louis Lions,et al.  Some Methods in the Mathematical Analysis of Systems and Their Control , 1981 .

[20]  Ivo Babuška,et al.  Solution of Interface Problems by Homogenization. I , 1976 .

[21]  Grégoire Allaire,et al.  BLOCH WAVE HOMOGENIZATION AND SPECTRAL ASYMPTOTIC ANALYSIS , 1998 .