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.

翻译：本文提出了一种边界修正的弱伽辽金混合有限元方法，用于求解具有曲线界面的二维区域中的椭圆界面问题。该方法基于贴体多边形网格构建，其中界面边为直线段，可能与实际物理曲线界面不完全吻合。为解决这一几何偏差，我们采用边界值修正技术，通过泰勒展开方法将界面条件从物理界面转移至近似界面。随后，诺伊曼界面条件在变分形式中以弱形式施加。该方法避免了在曲线单元上进行数值积分，从而降低了实现复杂度。我们证明了任意阶离散格式在能量范数下的最优阶收敛性，并提供了数值算例以验证理论结果。