Finite element approximation of a fourth order nonlinear degenerate parabolic equation. (English) Zbl 0913.65084

Barrett, John W.; Blowey, James F.; Garcke, Harald

Numer. Math. 80, No. 4, 525-556 (1998).

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.

Reviewer: Qin Mengzhao (Beijing)

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

Keywords:

finite elements; nonlinear degenerate parabolic equation; lubrication problem; convergence; numerical examples