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

Mingqing Chen; Jianguo Huang

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arXiv · 2608.12886

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

Mingqing Chen·Jianguo Huang

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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.

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Mingqing Chen, Jianguo Huang. 2026-08-13. A robust and optimal method for a sixth-order elliptic singular perturbation problem. https://arxiv.org/abs/2608.12886

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