Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 236, Issue -, Pages 74-80Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2012.12.001
Keywords
Cahn-Hilliard equation; FEM; Accuracy; Computational time; JFNK
Funding
- United States Nuclear Energy Advanced Modeling and Simulation program for Fundamental Methods and Modeling
- U.S. Government [DE-AC07-05ID14517]
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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. Published by Elsevier Inc.
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