Communications in Mathematical Sciences

Heterogeneous multiscale finite element method with novel numerical integration schemes

Rui Du and Pingbing Ming

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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.

Article information

Commun. Math. Sci., Volume 8, Number 4 (2010), 863-885.

First available in Project Euclid: 2 November 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 74Q05: Homogenization in equilibrium problems 74Q15: Effective constitutive equations 74Q20: Bounds on effective properties 39A12: Discrete version of topics in analysis

Heterogeneous multiscale method finite element method numerical integration schemes elliptic homogenization problems


Du, Rui; Ming, Pingbing. Heterogeneous multiscale finite element method with novel numerical integration schemes. Commun. Math. Sci. 8 (2010), no. 4, 863--885.

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