Stability and error analysis for a diffuse interface approach to an   advection-diffusion equation on a moving surface
  In this paper we analyze a fully discrete numerical scheme for solving a parabolic PDE on a moving surface. The method is based on a diffuse interface approach that involves a level set description of the moving surface. Under suitable conditions on the spatial grid size, the time step and the interface width we obtain stability and error bounds with respect to natural norms. Furthermore, we present test calculations that confirm our analysis. 
Klaus Deckelnick and Vanessa Styles
math.NA