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arXiv · 2307.07387

Locking-free HDG methods for Reissner-Mindlin plates equations on polygonal meshes

Gang Chen·Lu Zhang·Shangyou Zhang
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Abstract

We present and analyze a new hybridizable discontinuous Galerkin method (HDG) for the Reissner-Mindlin plate bending system. Our method is based on the formulation utilizing Helmholtz Decomposition. Then the system is decomposed into three problems: two trivial Poisson problems and a perturbed saddle-point problem. We apply HDG scheme for these three problems fully. This scheme yields the optimal convergence rate ($(k+1)$th order in the $\mathrm{L}^2$ norm) which is uniform with respect to plate thickness (locking-free) on general meshes. We further analyze the matrix properties and precondition the new finite element system. Numerical experiments are presented to confirm our theoretical analysis.

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Gang Chen, Lu Zhang, Shangyou Zhang. 2023-07-14. Locking-free HDG methods for Reissner-Mindlin plates equations on polygonal meshes. https://arxiv.org/abs/2307.07387

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