@article{GrRu00,
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 = {http://numod.ins.uni-bonn.de/research/papers/public/GrRu00.pdf 1}
}