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Finite element approximation of a fourth order nonlinear degenerate parabolic equation. (English) Zbl 0913.65084
The authors discussed a fully practical finite element approximation of the fourth-order nonlinear degenerate parabolic equation. \[ u_{t}+\nabla\cdot (b(u)\nabla\Delta u)=0 \] where \(b(u):=| u| ^{p}\) for any given \(p\in (0,\infty)\) well-posedness of approximation and convergence in one space dimension is proved. Some numerical experiments are illustrated.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
76D08 Lubrication theory
35K65 Degenerate parabolic equations
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