In:
European Journal of Applied Mathematics, Cambridge University Press (CUP), Vol. 12, No. 3 ( 2001-06), p. 293-320
Kurzfassung:
We present a finite element scheme for nonlinear fourth-order diffusion equations that arise
for example in lubrication theory for the time evolution of thin films of viscous fluids. The equations are in general fourth-order degenerate parabolic, but in addition singular terms of
second order may occur which model the effects of intermolecular forces or thermocapillarity. Discretizing the arising nonlinearities in a subtle way allows us to establish discrete counterparts
of the essential integral estimates found in the continuous setting. As a consequence, the algorithm is efficient, and results on convergence, nonnegativity or even strict positivity of
discrete solutions follow in a natural way. Applying this scheme to the numerical simulation of different models shows various interesting qualitative effects, which turn out to be in good
agreement with physical experiments.
Materialart:
Online-Ressource
ISSN:
0956-7925
,
1469-4425
DOI:
10.1017/S0956792501004429
Sprache:
Englisch
Verlag:
Cambridge University Press (CUP)
Publikationsdatum:
2001
ZDB Id:
2002906-8
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