A finite element method for elliptic problems with rapidly oscillating coefficients |
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Authors: | Wen-Ming He Jun-Zhi Cui |
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Institution: | (1) Department of Mathematics, Wenzhou University, Wenzhou, Zhejiang, 325035, P.R. China;(2) Institute of Computational Mathematics and Scientific/Engineering Computing, CAS, P.O. Box 2719, Beijing, 100080, P.R. China |
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Abstract: | In this paper, we consider solving second-order elliptic problems with rapidly oscillating coefficients. Under the assumption
that the oscillating coefficients are periodic, on the basis of classical homogenization theory, we present a finite element
method whose key is to combine a numerical approximation of the 1-order approximate solution of those equations and a numerical
approximation of the classical boundary corrector of those equations from different meshes exploiting the need for different
levels of resolution. Numerical experiments are included to illustrate the competitive behavior of the proposed finite element
method. |
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Keywords: | |
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