Transport and diffusion of material quantities on propagating interfaces via level set methods

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An h-narrow band finite-element method for elliptic equations on implicit surfaces (2010, methodology): “Previous works concerning finite-difference approximations have used Neumann and Dirichlet boundary conditions (Adalsteinsson & Sethian, 2003;Xu & Zhao, 2003;Greer,2006;Greer et al.,2006).”
A numerical method for two phase flows with insoluble surfactants (2011, methodology): “Adalsteinsson and Sethian [13] and Xu and Zhao [14] present numerical methods on how to solve for material quantities and surfactants, respectively, when the interface is represented using a level set function.”
Finite elements on evolving surfaces (2007, methodology): “An alternative approach to our method based on the use of (1.2) is to embed the surface in a family of level set surfaces (Bertalmio et al., 2001; Adalsteinsson & Sethian, 2003; Xu & Zhao, 2003; Greer et al., 2006).”
Analysis of trace finite element methods for surface partial differential equations (2015, methodology): “In Adalsteinsson & Sethian (2003) and Xu & Zhao (2003) numerical approaches were introduced that are based on extensions of PDEs off a two-dimensional surface to a three-dimensional neighbourhood of the surface.”