UNIFIED ANALYSIS OF LOW ORDER DISCONTINUOUS AND CONTINUOUS FINITE ELEMENT METHODS FOR THE REISSNER-MINDLIN PLATE
板的低阶间断与连续有限元法统一分析

Based on the discontinuous Galerkin method, a unified low-order formulation, which can apply to both continuous and discontinuous transverse displacement and rotation finite element spaces, is proposed for the Reissner-Mindlin plate problem. Piecewise constants are used to approximate the shear stress vectors. This scheme is stable, whether continuous or discontinuous finite element spaces are used to approximate the transverse displacement and the rotation. And is convergent uniformly with respect to thickness. The optimal H1 and L2 error bounds are proven. Finally, several low order finite element spaces are given for different cases. It is proved that most low order finite element spaces can be applied to our scheme. If there is at least one variable continuous, the spaces needed in our method are simpler than those of 1, 2].