A $C^0$ linear finite element method for sixth order elliptic equations

In this paper, we develop a straightforward $C^0$ linear finite element method for sixth-order elliptic equations. The basic idea is to use gradient recovery techniques to generate higher-order numerical derivatives from a $C^0$ linear finite element function. Both theoretical analysis and numerical experiments show that the proposed method has the optimal convergence rate under the energy norm. The method avoids complicated construction of conforming $C^2$ finite element basis or nonconforming penalty terms and has a low computational cost.