A Robust Solver for a Second Order Mixed Finite Element Method for the Cahn-Hilliard Equation
This provides an efficient solver for a second-order scheme, improving upon their prior first-order work, but is an incremental extension within computational PDEs.
The authors extend a robust solver from first-order to second-order mixed finite element splitting for the Cahn-Hilliard equation, achieving solver performance independent of mesh size and time step, with mild dependence on interfacial width.
We develop a robust solver for a second order mixed finite element splitting scheme for the Cahn-Hilliard equation. This work is an extension of our previous work in which we developed a robust solver for a first order mixed finite element splitting scheme for the Cahn-Hilliard equaion. 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.