A finite element method for Reissner-Mindlin plates

Duan, Huoyuan

doi:10.1090/S0025-5718-2013-02767-6

A finite element method for Reissner-Mindlin plates
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Math. Comp. 83 (2014), 701-733 Request permission

Abstract:

A finite element method is proposed and analyzed for the Reissner-Mindlin plate problem subject to various boundary conditions. Rotation and transverse displacement variables are approximated by continuous linear elements (enriched with local bubbles) and an $L^2$ projector is applied to the shear energy term onto the Raviart-Thomas $H(\mathrm {div};\Omega )$ finite element. Stability and optimal error bounds hold uniformly in the plate thickness.

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