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arXiv · 1503.06282

Continuous Piecewise Linear Finite Elements for the Kirchhoff-Love Plate Equation

Karl Larsson·Mats G. Larson
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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. 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/Basic Plate Triangle does not converge on unstructured meshes while the fully quadratic reconstruction show optimal convergence.

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Karl Larsson, Mats G. Larson. 2015-03-21. Continuous Piecewise Linear Finite Elements for the Kirchhoff-Love Plate Equation. https://doi.org/10.1007/s00211-011-0429-5

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