Nonconforming Immersed Finite Element Spaces For Elliptic Interface Problems

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.

References in corpus (1)

• A Group of Immersed Finite Element Spaces For Elliptic Interface Problems

Cited by in corpus (5)

• A Fixed Mesh Method With Immersed Finite Elements for Solving Interface Inverse Problems
• An Immersed Weak Galerkin Method For Elliptic Interface Problems
• A stabilized nonconforming Nitsche's extended finite element method for Stokes interface problems
• Analysis of nonconforming IFE methods and a new scheme for elliptic interface problems
• A Trilinear Immersed Finite Element Method for Solving Elliptic Interface Problems