author = {Gr{\"{u}}n, G{\"{u}}nther and Lenz, Martin and Rumpf, Martin},
  title = {A Finite Volume Scheme for Surfactant Driven Thin Film Flow},
  booktitle = {Finite Volumes for Complex Applications III},
  year = {2002},
  editor = {Herbin, R. and Kr{\"{o}}ner, D.},
  pages = {567--574},
  publisher = {Hermes Penton Sciences},
  abstract = {The flow of a thin viscous film under the influence of a surface active
	agent (surfactant) is described by a system of degenerate parabolic
	equations. A robust and effective numerical scheme based on a finite
	volume discretization in space and a suitable operator splitting
	in time is presented. The convective part, which models the effects
	of Marangoni forces, is treated by an higher order explicit up-wind
	scheme with a limited linear reconstruction. For the fourth order
	parabolic part, which corresponds to the classical thin film problem,
	we formulate a finite volume scheme that entails the same conservation
	properties continuous solutions have, i.e. energy and entropy estimates.
	The scheme and the fundamental estimates are derived in the relevant
	2D case. Numerical simulations and the convergence result are currently
	restricted to 1D.},
  pdf = { 1},
  isbn = {1-9039-9634-1}