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A type of multi-level correction scheme for eigenvalue problems by nonconforming finite element methods

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Abstract

In this paper, a type of multi-level correction scheme is proposed to solve eigenvalue problems by nonconforming finite element methods. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which only needs to solve a source problem on finer finite element space and an eigenvalue problem on a coarse finite element space. This correction scheme can improve the efficiency of solving eigenvalue problems by the nonconforming finite element method. Furthermore, the same as the direct eigenvalue solving by the nonconforming finite element method, this multi-level correction method can also produce the lower-bound approximations of the eigenvalues.

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Authors and Affiliations

  1. LSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Hehu Xie

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  1. Hehu Xie
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Correspondence to Hehu Xie.

Additional information

Communicated by Rolf Stenberg.

This work is supported in part by the National Science Foundation of China (NSFC 91330202, 11371026, 11001259, 11201501, 11031006, 2011CB309703), the National Center for Mathematics and Interdisciplinary Science, CAS and the President Foundation of AMSS-CAS.

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Xie, H. A type of multi-level correction scheme for eigenvalue problems by nonconforming finite element methods. Bit Numer Math 55, 1243–1266 (2015). https://doi.org/10.1007/s10543-015-0545-1

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  • DOI: https://doi.org/10.1007/s10543-015-0545-1

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