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Zbl 1190.65173
Hetmaniuk, Ulrich L.; Lehoucq, Richard B.
A special finite element method based on component mode synthesis. (English)
[J] ESAIM, Math. Model. Numer. Anal. 44, No. 3, 401-420 (2010). ISSN 0764-583X; ISSN 1290-3841/e

Summary: The goal of our paper is to introduce basis functions for the finite element discretization of a second order linear elliptic operator with rough or highly oscillating coefficients. The proposed basis functions are inspired by the classic idea of component mode synthesis and exploit an orthogonal decomposition of the trial subspace to minimize the energy. Numerical experiments illustrate the effectiveness of the proposed basis functions.

MSC 2000:: *65N30 Finite numerical methods (BVP of PDE)
35J25 Second order elliptic equations, boundary value problems
35J05 Laplace equation, etc.
65N55 Multigrid methods; domain decomposition (BVP of PDE)

Keywords: eigenvalues; modal analysis; multilevel; substructuring; domain decomposition; dimensional reduction; finite elements; Poisson equation; second order linear elliptic operator; highly oscillating coefficients; numerical experiments

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