Nonconforming immersed finite element spaces for elliptic interface problems
Nonconforming immersed finite element spaces for elliptic interface problems
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DOI：
10.1016/j.camwa.2017.10.040
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发表时间：
2016-12
期刊：
影响因子：
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通讯作者：
Ruchi Guo;Tao Lin;Xu Zhang
中科院分区：
文献类型：
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作者：
Ruchi Guo;Tao Lin;Xu Zhang
本文利用Chen和Zou（1998）提出的统一框架研究了两个具有积分值自由度的浸入有限元空间。界面单元的形函数是定义在由实际界面或其线近似分离的子单元上的分段多项式。在这个统一的框架中，我们使用著名的谢尔曼-莫里森系统的可逆性，以证明存在性和唯一性的IFE形函数的每个接口单元在矩形或三角形网格。此外，我们开发了一个多边展开分段函数和一组身份的IFE函数，使我们能够显示这些IFE空间的最佳逼近能力。
In this paper, we use a unified framework introduced in Chen and Zou (1998) to study two nonconforming immersed finite element (IFE) spaces with integral-value degrees of freedom. The shape functions on interface elements are piecewise polynomials defined on sub-elements separated either by the actual interface or its line approximation. In this unified framework, we use the invertibility of the well known Sherman–Morison systems to prove the existence and uniqueness of IFE shape functions on each interface element in either a rectangular or triangular mesh. Furthermore, we develop a multi-edge expansion for piecewise functions and a group of identities for nonconforming IFE functions which enable us to show the optimal approximation capability of these IFE spaces.