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Generalized Rayleigh quotient and finite element two-grid discretization schemes

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Abstract

This study discusses generalized Rayleigh quotient and high efficiency finite element discretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of exact eigenvalue with the ascent of finite element approximate eigenvalue. 3) Based on the work of Xu Jinchao and Zhou Aihui, finite element two-grid discretization schemes are established to solve nonselfadjoint elliptic differential operator eigenvalue problems and these schemes are used in both conforming finite element and nonconforming finite element. Besides, the efficiency of the schemes is proved by both theoretical analysis and numerical experiments. 4) Iterated Galerkin method, interpolated correction method and gradient recovery for selfadjoint elliptic differential operator eigenvalue problems are extended to nonselfadjoint elliptic differential operator eigenvalue problems.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang, 550001, China

    YiDu Yang & XinYue Fan

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  1. YiDu Yang
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  2. XinYue Fan
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Correspondence to YiDu Yang.

Additional information

This work was supported by National Natural Science Foundation of China (Grant No. 10761003) and the Governor’s Special Foundation of Guizhou Province for Outstanding Scientific Education Personnel (Grant No. [2005]155)

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Yang, Y., Fan, X. Generalized Rayleigh quotient and finite element two-grid discretization schemes. Sci. China Ser. A-Math. 52, 1955–1972 (2009). https://doi.org/10.1007/s11425-009-0016-8

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  • DOI: https://doi.org/10.1007/s11425-009-0016-8

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