A DDR method for the Reissner-Mindlin plate bending problem on polygonal meshes - Archive ouverte HAL Access content directly
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A DDR method for the Reissner-Mindlin plate bending problem on polygonal meshes

Jérôme Droniou
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Abstract

In this work we propose a discretisation method for the Reissner--Mindlin plate bending problem in primitive variables that supports general polygonal meshes and arbitrary order. The method is inspired by a two-dimensional discrete de Rham complex for which key commutation properties hold that enable the cancellation of the contribution to the error linked to the enforcement of the Kirchhoff constraint. Denoting by $k\ge 0$ the polynomial degree for the discrete spaces and by $h$ the meshsize, we derive for the proposed method an error estimate in $h^{k+1}$ for general $k$, as well as a locking-free error estimate for the lowest-order case $k=0$. The theoretical results are validated on a complete panel of numerical tests.
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Dates and versions

hal-03234088 , version 1 (25-05-2021)

Identifiers

  • HAL Id : hal-03234088 , version 1

Cite

Daniele Antonio Di Pietro, Jérôme Droniou. A DDR method for the Reissner-Mindlin plate bending problem on polygonal meshes. 2021. ⟨hal-03234088⟩
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