Barrett, John W.; Blowey, James F.; Garcke, Harald Finite element approximation of the Cahn-Hilliard equation with degenerate mobility. (English) Zbl 0947.65109 SIAM J. Numer. Anal. 37, No. 1, 286-318 (1999). A finite element approximation of the Cahn-Hilliard equation with degenerate mobility \[ {\partial u\over\partial t}= \nabla(b(u) \nabla(-\gamma\Delta u+ \Psi'(u))) \] is considered, where \(b(u)\geq 0\) is a diffusional mobility and \(\Psi(u)\) is a homogeneous free energy. Well-posedness and stability bounds for this approximation is shown and convergence in one space dimension is proved.An iterative scheme for solving the resulting nonlinear discrete system is analyzed and a method is discussed how this approximation has to be modified in order to be applicable to a logarithmic homogeneous free energy. Some numerical experiments are presented. Reviewer: Z.Dżygadło (Warszawa) Cited in 85 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 82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics 35K65 Degenerate parabolic equations 35K55 Nonlinear parabolic equations Keywords:fourth-order degenerate parabolic equation; phase separation; finite elements; convergence; Cahn-Hilliard equation; stability; iterative scheme; nonlinear discrete system; numerical experiments PDF BibTeX XML Cite \textit{J. W. Barrett} et al., SIAM J. Numer. Anal. 37, No. 1, 286--318 (1999; Zbl 0947.65109) Full Text: DOI OpenURL