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

  • Authors:

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

  • Affiliations:

  • -;-;-;-;-;-;-

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2013

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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 C^1-continuous basis functions or the equation is split into a pair of second-order PDEs, and discretized via C^0-continuous basis functions. In the current work, a quantitative comparison between C^1 Hermite and C^0 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.