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Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations

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Abstract

The paper deals with error estimates and lower bound approximations of the Steklov eigenvalue problems on convex or concave domains by nonconforming finite element methods. We consider four types of nonconforming finite elements: Crouzeix-Raviart, Q rot1 , EQ rot1 and enriched Crouzeix-Raviart. We first derive error estimates for the nonconforming finite element approximations of the Steklov eigenvalue problem and then give the analysis of lower bound approximations. Some numerical results are presented to validate our theoretical results.

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Authors and Affiliations

  1. LSEC, ICMSEC, Academy of Mathematics and Systems Science and Graduate University of Chinese Academy Sciences, Chinese Academy of Sciences, Beijing, 100190, P.R.China

    Qin Li, Qun Lin & Hehu Xie

Authors
  1. Qin Li
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  2. Qun Lin
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  3. Hehu Xie
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Correspondence to Qin Li.

Additional information

This work has been supported in part by the National Science Foundation of China (NSFC 11001259, 11031006, 2011CB309703).

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Li, Q., Lin, Q. & Xie, H. Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations. Appl Math 58, 129–151 (2013). https://doi.org/10.1007/s10492-013-0007-5

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