An immersed finite element space and its approximation capability

By Zhilin Li, Tao Lin, Yi Lin, R. Rogers. 2004

232 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/f64defd9cb43639244d3b1ac3b7f9b2c50ac9bf1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Xiaoming He
2. Yanping Lin
3. Tao Lin
4. Xu Zhang
5. Gunilla Kreiss
6. Eddie Wadbro
7. Sara Zahedi
8. Martin Berggren

In Computational Theory and Mathematics

1. Yanping Lin
2. Xiaoming He
3. Tao Lin
4. Hong Zheng
5. Wei Li
6. Xiu-li Du
7. Xu Zhang
8. Gunilla Kreiss

In Mechanics of Materials

1. Yanping Lin
2. Xiaoming He
3. Tao Lin
4. Wei Li
5. Hong Zheng
6. Xiu-li Du
7. Xu Zhang
8. Gunilla Kreiss

Citations in the corpus

• Immersed finite element methods for elliptic interface problems with non-homogeneous jump conditions (2011, methodology): “The recently developed immersed finite element (IFE) methods [1, 2, 8, 11, 13, 15, 16, 24, 25, 28, 30, 31, 32, 33, 34, 38, 41] also fall into this framework.”
• A uniformly well-conditioned, unfitted Nitsche method for interface problems (2013, methodology): “Examples of such methods are the immersed finite element methods IFEM [18,19], the extended finite element method XFEM [3,8,10,12], and the unfitted finite element method by Hansbo and Hansbo [13].”
• Three‐dimensional immersed finite element methods for electric field simulation in composite materials (2005, methodology): “1 of Reference [11] indicates that for i = 1, 2, 3, there exists a unique local nodal function i (r, z) defined by (11) such that i (Aj ) = { 1 when i = j 0 when i = j Then, we form the local FE space Sh(T ) in T as the linear space spanned by these local nodal basis functions i , i = 1, 2, 3.”
• A Bilinear Immersed Finite Volume Element Method For the Diffusion Equation with Discontinuous Coefficient (2009, methodology): “Similar phenomenon has been observed for IFE method, see [39,57].”
• Approximation capability of a bilinear immersed finite element space (2008, methodology): “First, let us recall two lemmas from [66].”
• The convergence of the bilinear and linear immersed finite element solutions to interface problems (2012, methodology): “The involved bilinear and linear IFE spaces were introduced in [1,2] and the approximation capability of the two IFE spaces were discussed in [3, 4].”
• Immersed finite element methods for parabolic equations with moving interface (2013, background): “Together with the jump conditions, we have [38, 39]:”
• Exact imposition of essential boundary condition and material interface continuity in Galerkin‐based meshless methods (2017, methodology): “[21] developed immersed interface elements to enforce the interface continuity condition.”