论文标题
椭圆界面问题的未固定混合有限元方法
Unfitted mixed finite element methods for elliptic interface problems
论文作者
论文摘要
在本文中，提出了新的未固定混合有限元素，以解决跳跃系数的椭圆界面问题。我们的模型基于具有分布式Lagrange乘数的虚拟域公式。当应用于流体结构相互作用问题的框架时，可以更好地看到我们的研究的相关性。提出了两个有限元素方案，具有分段恒定的Lagrange乘数，并从理论上证明了它们的稳定性。数值结果比较了这些元素的性能，确认了理论证明，并验证了该方案是否以最佳速率收敛。
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.
