Journal of Scientific Computing

, Volume 77, Issue 2, pp 1234–1249 | Cite as

A Robust Solver for a Mixed Finite Element Method for the Cahn–Hilliard Equation

  • Susanne C. Brenner
  • Amanda E. Diegel
  • Li-Yeng Sung


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.


Cahn–Hilliard equation Convex splitting Mixed finite element methods MINRES Block diagonal preconditioner Multigrid 



Portions of this research were conducted with high performance computational resources provided by Louisiana State University ( We would also like to thank Shawn Walker for his valuable advice regarding the FELICITY/C++ Toolbox for MATLAB.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Susanne C. Brenner
    • 1
  • Amanda E. Diegel
    • 1
  • Li-Yeng Sung
    • 1
  1. 1.Department of Mathematics and Center for Computation and TechnologyLouisiana State UniversityBaton RougeUSA

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