Year: 2020
Author: Dietmar Gallistl, Mira Schedensack
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 1 : pp. 1–13
Abstract
A numerical scheme for the Reissner–Mindlin plate model is proposed. The method is based on a discrete Helmholtz decomposition and can be viewed as a generalization of the nonconforming finite element scheme of Arnold and Falk [SIAM J. Numer. Anal., 26(6):1276-1290, 1989]. The two unknowns in the discrete formulation are the in-plane rotations and the gradient of the vertical displacement. The decomposition of the discrete shear variable leads to equivalence with the usual Stokes system with penalty term plus two Poisson equations and the proposed method is equivalent to a stabilized discretization of the Stokes system that generalizes the Mini element. The method is proved to satisfy a best-approximation result which is robust with respect to the thickness parameter $t$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1902-m2018-0166
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 1 : pp. 1–13
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Reissner–Mindlin plate Nonconforming finite element Discrete Helmholtz decomposition Robustness.