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

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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 Gx0ε, 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. © 2007 Elsevier Inc. All rights reserved.

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He, W. ming, & Cui, J. zhi. (2007). A new approximate method for second order elliptic problems with rapidly oscillating coefficients based on the method of multiscale asymptotic expansions. Journal of Mathematical Analysis and Applications, 335(1), 657–668. https://doi.org/10.1016/j.jmaa.2007.01.085

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