A quantitative comparison between C0 and C1 elements for solving the Cahn-Hilliard equation

Liangzhe Zhang, Michael Tonks, Derek Gaston, John W. Peterson, David Andrs, Paul C. Millett, Bulent S. Biner

Research output: Contribution to journalArticle

24 Scopus citations

Abstract

The Cahn-Hilliard (CH) equation is a time-dependent fourth-order partial differential equation (PDE). When solving the CH equation via the finite element method (FEM), the domain is discretized by C1-continuous basis functions or the equation is split into a pair of second-order PDEs, and discretized via C0-continuous basis functions. In the current work, a quantitative comparison between C1 Hermite and C0 Lagrange elements is carried out using a continuous Galerkin FEM formulation. The different discretizations are evaluated using the method of manufactured solutions solved with Newton's method and Jacobian-Free Newton Krylov. It is found that the use of linear Lagrange elements provides the fastest computation time for a given number of elements, while the use of cubic Hermite elements provides the lowest error. The results offer a set of benchmarks to consider when choosing basis functions to solve the CH equation. In addition, an example of microstructure evolution demonstrates the different types of elements for a traditional phase-field model.

Original languageEnglish (US)
Pages (from-to)74-80
Number of pages7
JournalJournal of Computational Physics
Volume236
Issue number1
DOIs
StatePublished - Mar 1 2013

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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    Zhang, L., Tonks, M., Gaston, D., Peterson, J. W., Andrs, D., Millett, P. C., & Biner, B. S. (2013). A quantitative comparison between C0 and C1 elements for solving the Cahn-Hilliard equation. Journal of Computational Physics, 236(1), 74-80. https://doi.org/10.1016/j.jcp.2012.12.001