A $C^0$ linear finite element method for sixth order elliptic equations
This provides a simpler and more efficient numerical method for solving high-order elliptic equations, which are important in applications like thin plate bending problems.
The authors developed a C0 linear finite element method for sixth-order elliptic equations using gradient recovery techniques, achieving optimal convergence rates under the energy norm with low computational cost.
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.