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Conforming finite element methods for the von Kármán equations

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Abstract

In this paper, we consider canonical von Kármán equations that describe the bending of thin elastic plates defined on polygonal domains. A conforming finite element method is employed to approximate the displacement and Airy stress functions. Optimal order error estimates in energy, H 1 and L 2 norms are deduced. The results of numerical experiments confirm the theoretical results obtained.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

    Gouranga Mallik & Neela Nataraj

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  1. Gouranga Mallik
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  2. Neela Nataraj
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Correspondence to Neela Nataraj.

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Communicated by: Charlie Elliott

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Mallik, G., Nataraj, N. Conforming finite element methods for the von Kármán equations. Adv Comput Math 42, 1031–1054 (2016). https://doi.org/10.1007/s10444-016-9452-5

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  • DOI: https://doi.org/10.1007/s10444-016-9452-5

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