This paper presents a lowest-order immersed Raviart-Thomas mixed triangular finite element method for solving elliptic interface problems on unfitted meshes independent of the interface. In order to achieve the optimal convergence rates on unfitted meshes, an immersed finite element finite (IFE) is constructed by modifying the traditional Raviart-Thomas element. Some important properties are derived including the unisolvence of IFE basis functions, the optimal approximation capabilities of the IFE space and the corresponding commuting digram. Optimal error estimates are rigorously proved for the mixed IFE method and some numerical examples are also provided to validate the theoretical analysis.

翻译：本文介绍了一种最低顺序浸泡在Raviart-Thomas混合三角有限要素法,用于解决与接口无关的不合格间歇物的椭圆界面问题。为了实现不合适间歇物的最佳趋同率,通过修改传统的Raviart-Thomas元素构建了一个浸入的有限要素(IFE),产生了一些重要的属性,包括IFE基础功能的不溶性、IFE空间的最佳近似能力以及相应的通勤二格;为混合的IFE方法严格证明了最佳误差估计,还提供了一些数字例子来验证理论分析。