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December 2010 Heterogeneous multiscale finite element method with novel numerical integration schemes
Rui Du, Pingbing Ming
Commun. Math. Sci. 8(4): 863-885 (December 2010).


In this paper we introduce two novel numerical integration schemes within the framework of the heterogeneous multiscale method (HMM), when the finite element method is used as the macroscopic solver, to resolve the elliptic problem with a multiscale coefficient. For nonself-adjoint elliptic problems, optimal convergence rate is proved for the proposed methods, which naturally yields a new strategy for refining the macro-micro meshes and a criterion for determining the size of the microcell. Numerical results following this strategy show that the new methods significantly reduce the computational cost without loss of accuracy.


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Rui Du. Pingbing Ming. "Heterogeneous multiscale finite element method with novel numerical integration schemes." Commun. Math. Sci. 8 (4) 863 - 885, December 2010.


Published: December 2010
First available in Project Euclid: 2 November 2010

zbMATH: 1210.65189
MathSciNet: MR2744910

Primary: 39A12 , 65N30 , 74Q05 , 74Q15 , 74Q20

Keywords: elliptic homogenization problems , finite element method , Heterogeneous multiscale method , numerical integration schemes

Rights: Copyright © 2010 International Press of Boston

Vol.8 • No. 4 • December 2010
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