A Nonconforming Finite Element Method for Elliptic Interface Problems on Locally Anisotropic Meshes
Abstract
We propose a new nonconforming finite element method for elliptic interface problems. The method is constructed on a locally anisotropic mixed mesh, which is generated by fitting the interface through a simple connection of intersection points on an interface-unfitted background mesh, as introduced in \cite{Hu2021optimal}. We first establish interpolation error estimates on quadrilateral elements satisfying the regular decomposition property (RDP). Building on this, the main contribution of this work is a novel consistency error analysis for nonconforming elements, which removes the quasi-regularity assumption commonly required in existing approaches. Numerical results confirm the theoretical convergence rates and demonstrate the robustness and accuracy of the proposed method.
Cite
@article{arxiv.2506.15077,
title = {A Nonconforming Finite Element Method for Elliptic Interface Problems on Locally Anisotropic Meshes},
author = {Chenchen Geng and Hua Wang and Qichen Zhang},
journal= {arXiv preprint arXiv:2506.15077},
year = {2025}
}