Locking-free HDG methods for Reissner-Mindlin plates equations on polygonal meshes
Numerical Analysis
2023-07-17 v1 Numerical Analysis
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 (th order in the 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.
Keywords
Cite
@article{arxiv.2307.07387,
title = {Locking-free HDG methods for Reissner-Mindlin plates equations on polygonal meshes},
author = {Gang Chen and Lu Zhang and Shangyou Zhang},
journal= {arXiv preprint arXiv:2307.07387},
year = {2023}
}