This paper presents a new weak Galerkin (WG) method for elliptic interface problems on general curved polygonal partitions. The method's key innovation lies in its ability to transform the complex interface jump condition into a more manageable Dirichlet boundary condition, simplifying the theoretical analysis significantly. The numerical scheme is designed by using locally constructed weak gradient on the curved polygonal partitions. We establish error estimates of optimal order for the numerical approximation in both discrete $H^1$ and $L^2$ norms. Additionally, we present various numerical results that serve to illustrate the robust numerical performance of the proposed WG interface method.

翻译：本文提出了一种新的弱伽辽金（WG）方法，用于在一般曲边多边形分区上求解椭圆界面问题。该方法的关键创新在于能够将复杂的界面跳跃条件转化为更易处理的狄利克雷边界条件，从而显著简化了理论分析。数值格式通过在曲边多边形分区上局部构造弱梯度来设计。我们在离散$H^1$和$L^2$范数下建立了数值近似的最优阶误差估计。此外，我们给出了各种数值结果，以展示所提出的WG界面方法稳健的数值性能。