2025/06/18 by Chenchen Geng, Hua Wang, Geng, Chenchen +3
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2506.15077
openalex publication_date 2025/06/18 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28
We propose a new nonconforming \(P1\) 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 \citeHu2021optimal. 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.