A ROBUST DISCRETIZATION OF THE REISSNER-MINDLIN PLATE WITH ARBITRARY POLYNOMIAL DEGREE

作     者：Dietmar Gallistl Mira Schedensack Dietmar Gallistl;Mira Schedensack

作者机构：Friedrich-Schiller-Universitdt Jena07737 JenaGermany Universitat LeipzigPF 10092004009 LeipzigGermany 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2020年第38卷第1期

页      面：1-13页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：The first author was supported by the Deutsche Forschungsgemeinschaft(DFG)through SFB support by the DFG Priority Program 1748 under the project "Robust and Efficient Finite Element Discretizations for Higher-Order Gradient Formulations" 

主　　题：Reissner-Mindlin plate Nonconforming finite element Discrete Helmholtz decomposition Robustness 

摘      要：A numerical scheme for the Reissner-Mindlin plate model is *** method is based on a discrete Helmholtz decomposition and can be viewed as a generalization of the nonconforming finite element scheme of Arnold and Falk[SIAM ***.,26(6):1276-1290,1989].The two unknowns in the discrete formulation are the in-plane rotations and the gradient of the vertical *** decomposition of the discrete shear variable leads to equivalence with the usual Stokes system with penalty term plus two Poisson equations and the proposed method is equivalent to a stabilized discretization of the Stokes system that generalizes the Mini *** method is proved to satisfy a best-approximation result which is robust with respect to the thickness parameter t.