A robust and optimal method for a sixth-order elliptic singular perturbation problem

Abstract

In this paper we propose a robust nonconforming finite method for a gradient-elastic Kirchhoff plate (GEKP) model with a small parameter $0<\iota <1$. While the method employs an $H^3$ cubic finite element for the discrete space, it employs an interpolation mapping into an $H^2$ nonconforming finite element space in both the lower-order terms of the bilinear form and the right-hand side. Notably, the numerical method is robust with respect to the parameter $\iota$ and uniformly convergent to order $h$ without any stabilized terms. Finally, some numerical experiments are performed to verify the theoretical findings.