A locking-free weak Galerkin finite element method for Reissner–Mindlin plate on polygonal meshes. (1st September 2020)

• Record Type: Journal Article
• Authors: Ye, Xiu; Zhang, Shangyou; Zhang, Zhimin
• Is Part Of: Computers & mathematics with applications. Volume 80:issue 5(2020)
• Page Start: 906
• Page End: 916
• Publication Date: 2020-09-01
• Subjects: Weak Galerkin -- Finite element methods -- Discrete gradient -- The Reissner–Mindlin plate -- Polygonal meshes; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2020.05.015
• Languages: English
• ISSNs: 0898-1221

Abstract

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.