In this paper, we develop a new weak Galerkin finite element scheme for the Stokes interface problem with curved interfaces. We take a unique vector-valued function at the interface and reflect the interface condition in the variational problem. Theoretical analysis and numerical experiments show that the errors can reach the optimal convergence order under the energy norm and $L^2$ norm.

翻译：本文针对具有曲线界面的Stokes界面问题，提出了一种新的弱Galerkin有限元格式。我们在界面处引入唯一的向量值函数，并将界面条件反映在变分问题中。理论分析与数值实验表明，误差在能量范数和$L^2$范数下均可达到最优收敛阶。