In this paper, new unfitted mixed finite elements are presented for elliptic interface problems with jump coefficients. Our model is based on a fictitious domain formulation with distributed Lagrange multiplier. The relevance of our investigations is better seen when applied to the framework of fluid structure interaction problems. Two finite elements schemes with piecewise constant Lagrange multiplier are proposed and their stability is proved theoretically. Numerical results compare the performance of those elements, confirming the theoretical proofs and verifying that the schemes converge with optimal rate.

翻译：在本文中,提出了新的不适于使用的混合有限要素,以解决与跳动系数的椭圆界面问题。我们的模型以分布式拉格朗格乘数的虚构域配方为基础。当我们的调查应用到流体结构互动问题框架时,人们会更清楚地看到我们调查的相关性。提出了两种带有片状恒定拉格朗格乘数的有限要素计划,并在理论上证明了其稳定性。数字结果比较了这些要素的性能,确认了理论证据,并核实这些计划与最佳率一致。