A locking-free weak Galerkin finite element method for Reissner–Mindlin plate on polygonal meshes. (1st September 2020) - Ye, Xiu; Zhang, Shangyou; Zhang, Zhimin
Abstract: A new weak Galerkin finite element method is introduced and analyzed for the Reissner–Mindlin plate model in the primary form (without introducing shear strain as an extra unknown), which results in a linear system with symmetric positive definite stiffness matrix. The proposed method achieves uniform convergence with respect to plate thickness (the so-called locking-free) without introducing any projection, reduced integration, etc. In addition, the new method can be applied to general polygonal meshes; in particular, we implement pentagonal and hexagonal meshes in our numerical tests. The numerical study confirms our theory.