2025/02/05 by Yongli Hou, Yi Liu, Hou, Yongli +3
Computer Science · Engineering · #65N12 #65N22 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2502.03157
openalex publication_date 2025/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a boundary-corrected weak Galerkin mixed finite element method for solving elliptic interface problems in 2D domains with curved interfaces. The method is formulated on body-fitted polygonal meshes, where interface edges are straight and may not align exactly with the curved physical interface. To address this discrepancy, a boundary value correction technique is employed to transfer the interface conditions from the physical interface to the approximate interface using a Taylor expansion approach. The Neumann interface condition is then weakly imposed in the variational formulation. This approach eliminates the need for numerical integration on curved elements, thereby reducing implementation complexity. We establish optimal-order convergence in the energy norm for arbitrary-order discretizations. Numerical results are provided to support the theoretical findings.