Finite Element Method Coupling Penalty Method for Flexural Shell Model

In this paper, we propose a conforming finite element method coupling penalty method for the linearly elastic flexural shell to overcome computational difficulties. We start with discretizing the displacement variable, i.e., the two tangent components of the displacement are discretized by using conforming finite elements (linear element), and the normal component of the displacement is discretized by using conforming Hsieh-Clough-Tocher element (HCT element). Then, the existence, uniqueness, stability, convergence and a priori error estimate of the corresponding analyses are proven and analyzed. Finally, we present numerical experiments with a portion of the conical shell and a portion of the cylindrical shell to verify theoretical convergence results and demonstrate the effectiveness of the numerical scheme.