We develop a robust solver for a mixed finite element convex splitting scheme for the Cahn–Hilliard equation. The key ingredient of the solver is a preconditioned minimal residual algorithm (with a multigrid preconditioner) whose performance is independent of the spacial mesh size and the time step size for a given interfacial width parameter. The dependence on the interfacial width parameter is also mild.
Publication Source (Journal or Book title)
Journal of Scientific Computing
Brenner, S., Diegel, A., & Sung, L. (2018). A Robust Solver for a Mixed Finite Element Method for the Cahn–Hilliard Equation. Journal of Scientific Computing, 77 (2), 1234-1249. https://doi.org/10.1007/s10915-018-0753-3