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arXiv · 2501.12137

Robust and Optimal Mixed Methods for a Fourth-Order Elliptic Singular Perturbation Problem

Xuehai Huang·Zheqian Tang
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Abstract

A series of robust and optimal mixed methods based on two mixed formulations of the fourth-order elliptic singular perturbation problem are developed in this paper. First, a mixed method based on a second-order system is proposed without relying on Nitsche's technique or interpolations. Robust and optimal error estimates are derived using an $L^2$-bounded interpolation operator for tensors. Then, its connections to other discrete methods, including weak Galerkin methods and a mixed finite element method based on a first-order system, are established. Finally, numerical experiments are provided to validate the theoretical results.

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Xuehai Huang, Zheqian Tang. 2025-01-21. Robust and Optimal Mixed Methods for a Fourth-Order Elliptic Singular Perturbation Problem. https://arxiv.org/abs/2501.12137

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