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Adaptive finite element algorithms for eigenvalue problems based on local averaging type a posteriori error estimates

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Abstract

The local averaging technique has become a popular tool in adaptive finite element methods for solving partial differential boundary value problems since it provides efficient a posteriori error estimates by a simple postprocessing. In this paper, the technique is introduced to solve a class of symmetric eigenvalue problems. Its efficiency and reliability are proved by both the theory and numerical experiments structured meshes as well as irregular meshes.

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Authors and Affiliations

  1. Department of Mathematics, Syracuse University, 215 Carmegie Hall, Syracuse, NY, 13244-1150, USA

    Dong Mao

  2. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, PO Box 2719, Beijing, 100080, China

    Lihua Shen & Aihui Zhou

Authors
  1. Dong Mao
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  2. Lihua Shen
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  3. Aihui Zhou
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Additional information

Communicated by Yueshong Xu

Dedicated to Charles A. Micchelli on his 60th birthday

Mathematics subject classifications (2000)

65N15, 65N25, 65N30, 65N50.

Subsidized by the Special Funds for Major State Basic Research Projects, and also supported in part by the Chinese National Natural Science Foundation and the Knowledge Innovation Program of the Chinese Academy of Sciences.

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Mao, D., Shen, L. & Zhou, A. Adaptive finite element algorithms for eigenvalue problems based on local averaging type a posteriori error estimates. Adv Comput Math 25, 135–160 (2006). https://doi.org/10.1007/s10444-004-7617-0

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  • DOI: https://doi.org/10.1007/s10444-004-7617-0

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