In:
European Journal of Applied Mathematics, Cambridge University Press (CUP), Vol. 12, No. 3 ( 2001-06), p. 293-320
Abstract:
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.
Type of Medium:
Online Resource
ISSN:
0956-7925
,
1469-4425
DOI:
10.1017/S0956792501004429
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2001
detail.hit.zdb_id:
2002906-8
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