2025/09/16 by Chen, Yuan, Zhang, Xu
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2509.12555
In this paper, we introduce an immersed C0 interior penalty method for solving two-dimensional biharmonic interface problems on unfitted meshes. To accommodate the biharmonic interface conditions, high-order immersed finite element (IFE) spaces are constructed in the least-squares sense. We establish key properties of these spaces including unisolvency and partition of unity are, and verify their optimal approximation capability. These spaces are further incorporated into a modified C0 interior penalty scheme with additional penalty terms on interface segments. The well-posedness of the discrete solution is proved. Numerical experiments with various interface geometries confirm optimal convergence of the proposed method in L2, H1 and H2 norms.