A Family of Discontinuous Galerkin Finite Elements for the Reissner--Mindlin Plate

Authors:
Douglas N. Arnold;Franco Brezzi;L. Donatella Marini
Affiliations:
Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, USA 55455;Dipartimento di Matematica, Università di Pavia, IMATI-CNR, Pavia, Italy 27100;Dipartimento di Matematica, Università di Pavia, IMATI-CNR, Pavia, Italy 27100
Venue:
Journal of Scientific Computing
Year:
2005

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Abstract

We develop a family of locking-free elements for the Reissner--Mindlin plate using Discontinuous Galerkin (DG) techniques, one for each odd degree, and prove optimal error estimates. A second family uses conforming elements for the rotations and nonconforming elements for the transverse displacement, generalizing the element of Arnold and Falk to higher degree.