Asymptotic analysis of second-order boundary layer correctors

References

• Sanchez-Palencia , E . 1980 . Non-Homogeneous Media and Vibration Theory , Berlin : Springer Verlag .
   Google Scholar
• Jikov , VV , Kozlov , SM and Oleinik , OA . 1994 . Homogenization of Differential Operators and Integral Functionals , Berlin : Springer-Verlag .
   Google Scholar
• Bakhvalov , NS and Panasenko , GP . 1984 . Homogenization: Averaging Processes in Periodic Media , Nauka : Moscow . (in Russian) (English transl., Kluwer, Dordrecht/Boston/London, 1989)
   Google Scholar
• Bensoussan , A , Lions , J-L and Papanicolaou , G . 1978 . Asymptotic Analysis for Periodic Structures , Amsterdam : North Holland .
   Google Scholar
• Stein , E . 1971 . Singular Integrals and Differentiability Properties of Functions , Princeton , NJ : Princeton University Press .
   Google Scholar
• Lions , JL . 1981 . Some Methods in the Mathematical Analysis of Systems and Their Controls , Beijing, New York : Science Press, Gordon and Breach .
   Google Scholar
• Griso , G . 2004 . Error estimate and unfolding for periodic homogenization . Asymptotic Anal. , 40 : 269 – 286 .
   Web of Science ®Google Scholar
• Cioranescu , D , Damlamian , A and Griso , G . 2002 . Periodic unfolding and homogenization . C. R. Acad. Sci. Paris, Ser. I , 335 : 99 – 104 .
   Web of Science ®Google Scholar
• Moskow , S and Vogelius , M . 1997 . First-order corrections to the homogenised eigenvalues of a periodic composite medium. A convergence proof . Proc. Roy. Soc. Edinburgh , 127A : 1263 – 1299 .
   Google Scholar
• Allaire , G and Amar , M . 1999 . Boundary layer tails in periodic homogenization . ESAIM: Control, Optim. Calc. Variations , 4 : 209 – 243 .
   Google Scholar
• Versieux , H and Sarkis , M . 2008 . Convergence analysis for the numerical boundary corrector for elliptic equations with rapidly oscillating coefficients . SIAM J. Num. An. , 46 : 545 – 576 .
   Web of Science ®Google Scholar
• Onofrei , D and Vernescu , B . 2007 . Error estimates in periodic homogenization with non-smooth coefficients . Asymptotic Anal. , 54 : 103 – 123 .
   Web of Science ®Google Scholar
• Avellaneda , M and Lin , F-H . 1987 . Homogenization of elliptic problems with L p boundary data . Appl. Math. Optim. , 15 : 93 – 107 .
   Web of Science ®Google Scholar
• Tartar , L . Cours Peccot au College de France, 1977
   Google Scholar
• Cioranescu , D and Donato , P . 1999 . An Introduction to Homogenization , Oxford : Oxford University Press .
   Google Scholar
• Griso , G . 2006 . Interior error estimate for periodic homogenization . Anal. Appl. , 4 ( 1 ) : 61 – 80 .
   Web of Science ®Google Scholar
• Ladyzhenskaya , OA and Ural'tseva , NN . 1968 . Linear and Quasilinear Elliptic Equations , New York : Academic Press .
   Google Scholar
• Onofrei , D and Vernescu , B . Asymptotic Analysis of Boundary Layer Correctors and Applications – Extended version, arXiv:0812.4788 (2011)
   Google Scholar
• Girault , V and Raviart , PA . 1986 . Finite Element Methods for Navier–Stokes Equations , New York : Springer-Verlag .
   Google Scholar
• Byun , Sun-Sig . 2004 . Elliptic equations with BMO coefficients in Lipschitz domains . Trans. AMS , 357 ( 3 ) : 1025 – 1046 .
   Web of Science ®Google Scholar
• Li , YY and Vogelius , M . 2000 . Gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients . Arch. Rational Mech. Anal. , 153 : 91 – 151 .
   Web of Science ®Google Scholar
• Grisvard , P . 1985 . Elliptic Problems in Non-smooth Domains , London : Pitman .
   Google Scholar