Communications in Mathematical Sciences
- Commun. Math. Sci.
- Volume 8, Number 4 (2010), 863-885.
Heterogeneous multiscale finite element method with novel numerical integration schemes
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.
Commun. Math. Sci., Volume 8, Number 4 (2010), 863-885.
First available in Project Euclid: 2 November 2010
Permanent link to this document
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
Du, Rui; Ming, Pingbing. Heterogeneous multiscale finite element method with novel numerical integration schemes. Commun. Math. Sci. 8 (2010), no. 4, 863--885. https://projecteuclid.org/euclid.cms/1288725262