论文标题
双线性对多域和三个结点的椭圆界面问题的部分损坏的有限元方法
A Bilinear Partially Penalized Immersed Finite Element Method for Elliptic Interface Problems with Multi-Domains and Triple-Junction Points
论文作者
论文摘要
在本文中，我们介绍了一种新的部分惩罚的有限元方法（IFEM），以解决具有多域和三个结点的椭圆界面问题。我们在与多个接口或三连接点相交的元素上构建新的IFE功能，以适应接口跳跃条件。对于非均匀通量跳跃，我们通过添加三个局部通量基函数来丰富局部近似空间。进行数值实验以表明Lagrange插值和部分惩罚的IFEM解决方案在L2和H1规范中最佳地收敛。
In this article, we introduce a new partially penalized immersed finite element method (IFEM) for solving elliptic interface problems with multi-domains and triple-junction points. We construct new IFE functions on elements intersected with multiple interfaces or with triple-junction points to accommodate interface jump conditions. For non-homogeneous flux jump, we enrich the local approximating spaces by adding up to three local flux basis functions. Numerical experiments are carried out to show that both the Lagrange interpolations and the partial penalized IFEM solutions converge optimally in L2 and H1 norms.
