An Extended Finite Element Method for Two-Phase Fluids

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Stress concentration minimization of 2D filets using X-FEM and level set description (2007, methodology): “(9) interpolates linear ly the Level Set when first order finite element are used.”
A review of extended/generalized finite element methods for material modeling (2009, background): “Such applications were first proposed in Chessa and Belytschko [24, 23, 22].”
The extended/generalized finite element method: An overview of the method and its applications (2010, methodology): “Moving closed interfaces in the XFEM are e.g. found in Chessa and Belytschko [47] and Fries [77] for twophase flow problems and in Chessa et al. [50] for solidification problems.”
The extended finite element method in thermoelastic fracture mechanics (2008, background): “Such functions enrich the displacement field in References [18, 26–29] in order to represent material interfaces.”
Spatially adaptive techniques for level set methods and incompressible flow (2006, background): “Other interesting work includes the adaptive mesh redistribution of [93] and the finite element based fluids of [94, 19, 18].”
Strain smoothing in FEM and XFEM (2010, methodology): “XFEM was used successfully for crack propagation and other fields in computational physics [23,25,24,26,33].”