author = {Gr{\"{u}}n, G. and Rumpf, M.},
  title = {Nonnegativity Preserving Convergent Schemes for the Thin Film Equation},
  journal = {Numerische Mathematik},
  year = {2000},
  volume = {87},
  pages = {113--152},
  abstract = {We present numerical schemes for fourth order degenerate parabolic
	equations that arise e.g. in lubrication theory for time evolution
	of thin films of viscous fluids. We prove convergence and nonnegativity
	results in arbitrary space dimensions. A proper choice of the discrete
	mobility enables us to establish discrete counterparts of the essential
	integral estimates known from the continuous setting. Hence, the
	numerical cost in each time step reduces to the solution of a linear
	system involving a sparse matrix. Furthermore, by introducing a time
	step control that makes use of an explicit formula for the normal
	velocity of the free boundary we keep the numerical cost for tracing
	the free boundary low.},
  pdf = { 1}