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：本文针对具有跳跃系数的椭圆界面问题，提出了一种新的非拟合混合有限元方法。该模型基于带有分布拉格朗日乘子的虚拟区域公式。当应用于流固耦合问题的框架时，本研究的关联性更为显著。本文提出了两种具有分片常数拉格朗日乘子的有限元格式，并从理论上证明了其稳定性。数值结果比较了这些单元的性能，证实了理论证明，并验证了这些格式以最优速率收敛。