Barrett, John W.; Blowey, James F.; Garcke, Harald Finite element approximation of a fourth order nonlinear degenerate parabolic equation. (English) Zbl 0913.65084 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) Cited in 1 ReviewCited in 31 Documents 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 PDF BibTeX XML Cite \textit{J. W. Barrett} et al., Numer. Math. 80, No. 4, 525--556 (1998; Zbl 0913.65084) Full Text: DOI