Gräser, Carsten; Kornhuber, Ralf; Sack, Uli Nonsmooth Schur-Newton methods for multicomponent Cahn-Hilliard systems. (English) Zbl 1316.65086 IMA J. Numer. Anal. 35, No. 2, 652-679 (2015). The authors consider large scale nonlinear saddle point problems as arising by discretization of multicomponent Cahn-Hilliard systems with logarithmic and obstacle potentials. The discrete problems are obtained by semi-implicit discretization in time and a first-order finite element discretization in space. They incorporate the linear constraints that enforce solutions to stay on the Gibbs simplex using Lagrangian multipliers and prove the existence of these multipliers under the assumption of a non-trivial initial condition for the order parameters. The method is globally convergent, mesh independent, and robust with respect to the number of components and the occurring nonlinearities. Reviewer: Qin Meng Zhao (Beijing) Cited in 6 Documents MSC: 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 35Q35 PDEs in connection with fluid mechanics 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs Keywords:phase field models; variational inequalities; finite elements; convex minimization; descent methods; multigrid methods; Schur-Newton method; convergence; large scale nonlinear saddle point problems; multicomponent Cahn-Hilliard systems PDFBibTeX XMLCite \textit{C. Gräser} et al., IMA J. Numer. Anal. 35, No. 2, 652--679 (2015; Zbl 1316.65086) Full Text: DOI Link