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Symmetric and conforming mixed finite elements for plane elasticity using rational bubble functions

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Abstract

We construct stable, conforming and symmetric finite elements for the mixed formulation of the linear elasticity problem in two dimensions. In our approach we add three divergence-free rational functions to piecewise polynomials to form the stress finite element space. The relation with the elasticity elements and a class of generalized \(C^1\) Zienkiewicz elements is also discussed.

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Acknowledgments

This work was supported by the National Science Foundation through Grant numbers DMS-0914596 (Guzmán) and DMS-1115421 (Neilan).

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Johnny Guzmán

  2. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA

    Michael Neilan

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  1. Johnny Guzmán
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  2. Michael Neilan
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Correspondence to Michael Neilan.

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Guzmán, J., Neilan, M. Symmetric and conforming mixed finite elements for plane elasticity using rational bubble functions. Numer. Math. 126, 153–171 (2014). https://doi.org/10.1007/s00211-013-0557-1

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  • DOI: https://doi.org/10.1007/s00211-013-0557-1

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