A Weak Galerkin Method for the Reissner–Mindlin Plate in Primary Form
- 155 Downloads
A new finite element method is developed for the Reissner–Mindlin equations in its primary form by using the weak Galerkin approach. Like other weak Galerkin finite element methods, this one is highly flexible and robust by allowing the use of discontinuous approximating functions on arbitrary shape of polygons and, at the same time, is parameter independent on its stability and convergence. Error estimates of optimal order in mesh size h are established for the corresponding weak Galerkin approximations. Numerical experiments are conducted for verifying the convergence theory, as well as suggesting some superconvergence and a uniform convergence of the method with respect to the plate thickness.
KeywordsWeak Galerkin Finite element methods Weak gradient The Reissner–Mindlin plate Polygonal partitions
Mathematics Subject ClassificationPrimary 65N15 65N30 Secondary 35J50
- 19.Wang, C., Wang, J.: A primal-dual weak Galerkin finite element method for second order elliptic equations in non-divergence form. Math. Comput. (2017). doi: 10.1090/mcom/3220
- 20.Wang, J., Ye, X.: A weak Galerkin finite element method for second-order elliptic problems. J. Comput. Appl. Math. 241, 103–115 (2013). arXiv:1104.2897v1
- 21.Wang, J., Ye, X.: A weak Galerkin mixed finite element method for second-order elliptic problems. Math. Comput. 83, 2101–2126 (2014). arXiv:1202.3655v1