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Three-scale finite element eigenvalue discretizations

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Abstract

Some three-scale finite element discretization schemes are proposed and analyzed in this paper for a class of elliptic eigenvalue problems on tensor product domains. With these schemes, the solution of an eigenvalue problem on a fine grid may be reduced to the solutions of eigenvalue problems on a relatively coarse grid and some partially mesoscopic grids, together with the solutions of linear algebraic systems on a globally mesoscopic grid and several partially fine grids. It is shown theoretically and numerically that this type of discretization schemes not only significantly reduce the number of degrees of freedom but also produce very accurate approximations.

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Authors and Affiliations

  1. LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    X. Gao & A. Zhou

  2. School of Applied Mathematics, Central University of Finance and Economics, Beijing, 100081, China

    F. Liu

Authors
  1. X. Gao
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  2. F. Liu
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  3. A. Zhou
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Correspondence to A. Zhou.

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AMS subject classification (2000)

65N15, 65N25, 65N30, 65N50

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Gao, X., Liu, F. & Zhou, A. Three-scale finite element eigenvalue discretizations . Bit Numer Math 48, 533–562 (2008). https://doi.org/10.1007/s10543-008-0189-5

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  • DOI: https://doi.org/10.1007/s10543-008-0189-5

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