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arXiv · 1612.01862

Nonconforming Immersed Finite Element Spaces For Elliptic Interface Problems

Ruchi Guo·Tao Lin·Xu Zhang
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Abstract

In this paper, we use a unified framework introduced in [3] to study two classes of 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 shape functions on each interface element in either 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 that these IFE spaces have the optimal approximation capability.

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Ruchi Guo, Tao Lin, Xu Zhang. 2016-12-06. Nonconforming Immersed Finite Element Spaces For Elliptic Interface Problems. https://doi.org/10.1016/j.camwa.2017.10.040

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