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：在本文中,我们为Stokes与曲线界面的界面问题开发了一个新的微弱的Galerkin有限元素计划。我们在界面上使用一种独特的矢量估值功能,并反映变异问题中的界面条件。理论分析和数字实验表明,错误可以达到能源规范下的最佳汇合顺序和2美元规范下的最佳汇合顺序。