(untitled) (Advances in Applied Mathematics and Mechanics, 2020)
In this paper, we study the mixed element schemes of the Reissner-Mindlin plate model and the Kirchhoff plate model in multiply-connected domains. Constructing a regular decomposition of H_0(rot,Ω) and a Helmholtz decomposition of its dual, we develop mixed formulations of the models which are equivalent to the primal ones respectively and which are uniformly stable. We then present frameworks of designing uniformly stable mixed finite element schemes and of generating primal finite element schemes from the mixed ones. Specific finite elements are given under the frameworks as an example, and the primal scheme obtained coincides with a Dur00e1n-Liberman scheme which was constructed originally on simply-connected domains. Optimal solvers are constructed for the schemes.