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An a priori error estimate for finite element discretizations in nonlinear elasticity for polyconvex materials under small loads

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Summary.

We prove optimal a priori error estimates in W 1,p for finite element minimizers of polyconvex energy functionals with small applied loads. The proof relies on a quantitative version of Zhang’s stability estimate (K. Zhang, Arch. Rat. Mech. Anal. 114 (1991), 95-117).

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Authors and Affiliations

  1. Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040, Vienna, Austria

    Carsten Carstensen

  2. Mathematics Department, University of Maryland, College Park, MD 20742, USA

    Georg Dolzmann

Authors
  1. Carsten Carstensen
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  2. Georg Dolzmann
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Corresponding author

Correspondence to Carsten Carstensen.

Additional information

Mathematics Subject Classification (2000):35G25, 73G25, 65N12

This project was initiated while GD visited the California Institute of Technology in Pasadena supported by AFOSR/MURI (F 49602-98-1-0433) in 98-99. A short visit of CC to the California Institute of Technology the was supported by the Powell Foundation.

14 September 1999

Revised: 20 April 2000

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Carstensen, C., Dolzmann, G. An a priori error estimate for finite element discretizations in nonlinear elasticity for polyconvex materials under small loads. Numer. Math. 97, 67–80 (2004). https://doi.org/10.1007/s00211-003-0481-x

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  • DOI: https://doi.org/10.1007/s00211-003-0481-x

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