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A new approximate method for second order elliptic problems with rapidly oscillating coefficients based on the method of multiscale asymptotic expansions

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
335
Issue
1
Identifiers
DOI: 10.1016/j.jmaa.2007.01.085
Keywords
  • The Method Of Multiscale Asymptotic Expansions
  • Second Order Elliptic Equations With Rapidly Oscillating Coefficients
  • Error Estimate

Abstract

Abstract In this paper, we consider second order elliptic problems with rapidly oscillating coefficients. On basis of [O.A. Oleinik, A.S. Shamaev, G.A. Yosifian, Mathematical Problems in Elasticity and Homogenization, North-Holland, Amsterdam, 1992; Wen-ming He, Jun-zhi Cui, A pointwise estimate on the 1-order approximation of G x 0 ε , IMA J. Appl. Math. 70 (2005) 241–269] we propose a new approximate method to solve these problems. Of course, we present its error estimate.

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