New Cartesian grid methods for interface problems using the finite element formulation

By Zhilin Li, Tao Lin, Xiao-hui Wu. Numerische Mathematik, 2003

499 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/618a58ef529fce3bac6f6abff6b6fa7c50316f03

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. Peter Hansbo
5. Anita Hansbo
6. Gunilla Kreiss
7. Sara Zahedi
8. Eddie Wadbro

In Electrical and Electronic Engineering

1. Yanping Lin
2. Xiaoming He
3. Slimane Adjerid
4. Peter Hansbo
5. Anita Hansbo
6. Gunilla Kreiss
7. Eddie Wadbro
8. Sara Zahedi

In Mechanics of Materials

1. Yanping Lin
2. Xiaoming He
3. Tao Lin
4. Peter Hansbo
5. Anita Hansbo
6. Slimane Adjerid
7. Xu Zhang
8. Gunilla Kreiss

Citations in the corpus

• A p-th degree immersed finite element for boundary value problems with discontinuous coefficients (2009, methodology): “It has been shown [15, 16, 17, 18] that, for elliptic interface problems (including two or three dimensional problems), linear IFE functions on an interface element are uniquely determined by the nodal values and the interface jump conditions.”
• Approximation capability of a bilinear immersed finite element space (2008, methodology): “The recently developed immersed flnite element (IFE) methods [1, 2, 21, 29, 40, 41, 47, 49, 50 , 51, 52, 67, 70] also fall into the general framework of Babu•ska and J.E.”
• 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].”
• An unfitted finite element method, based on Nitsche's method, for elliptic interface problems (2002, methodology): “Here we considered a less trivial two-dimensional example (from [7]).”
• ON THE ACCURACY OF FINITE DIFFERENCE METHODS FOR ELLIPTIC PROBLEMS WITH INTERFACES (2006, unknown): “Communications in Applied Mathematics and Computational Science mathematical sciences publishers 1 Volume 1 No. 1 2006”
• Three‐dimensional immersed finite element methods for electric field simulation in composite materials (2005, methodology): “Therefore, the local nodal basis functions we want to construct for the 3-D axis-symmetrical interface problem are the same as those developed for the general 2-D interface problems in References [11, 12].”
• Immersed finite element methods for parabolic equations with moving interface (2013, background): “Together with the jump conditions, we have [38, 39]:”
• 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.”