×

Nonsmooth Schur-Newton methods for multicomponent Cahn-Hilliard systems. (English) Zbl 1316.65086

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.

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
PDFBibTeX XMLCite
Full Text: DOI Link