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Numerische Mathematik

, Volume 121, Issue 1, pp 65–97 | Cite as

Continuous piecewise linear finite elements for the Kirchhoff–Love plate equation

  • Karl LarssonEmail author
  • Mats G. Larson
Article

Abstract

A family of continuous piecewise linear finite elements for thin plate problems is presented. We use standard linear interpolation of the deflection field to reconstruct a discontinuous piecewise quadratic deflection field. This allows us to use discontinuous Galerkin methods for the Kirchhoff–Love plate equation. Three example reconstructions of quadratic functions from linear interpolation triangles are presented: a reconstruction using Morley basis functions, a fully quadratic reconstruction, and a more general least squares approach to a fully quadratic reconstruction. The Morley reconstruction is shown to be equivalent to the basic plate triangle (BPT). Given a condition on the reconstruction operator, a priori error estimates are proved in energy norm and L 2 norm. Numerical results indicate that the Morley reconstruction/BPT does not converge on unstructured meshes while the fully quadratic reconstruction show optimal convergence.

Mathematics Subject Classification (2000)

74S05 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsUmeå UniversityUmeåSweden

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