论文标题
用于椭圆界面问题的扩展混合有限元方法
An extended mixed finite element method for elliptic interface problems
论文作者
论文摘要
在本文中，我们提出了一种用于椭圆界面问题的扩展混合有限元方法。通过添加一些稳定术语，我们提出了一种基于Brezzi-Douglas-Marini元素空间和分段常数函数空间的混合近似形式，并表明离散的INF-SUP常数与界面相交三角剖分的方式无关。此外，我们得出最佳收敛性独立于界面相对于网格的位置。最后，提出了一些数值示例，以验证我们的理论结果。
In this paper, we propose an extended mixed finite element method for elliptic interface problems. By adding some stabilization terms, we present a mixed approximation form based on Brezzi-Douglas-Marini element space and the piecewise constant function space, and show that the discrete inf-sup constant is independent of how the interface intersects the triangulation. Furthermore, we derive that the optimal convergence holds independent of the location of the interface relative to the mesh. Finally, some numerical examples are presented to verify our theoretical results.
