Isogeometric analysis of the Cahn-Hilliard equation - a convergence study
M. Kaestner, P. Metsch, R. de Borst,
Volume: 305. Pages: 360--371
DOI: 10.1016/j.jcp.2015.10.047
Published: 2015
Abstract
Herein, we present a numerical convergence study of the Cahn-Hilliard
phase-field model within an isogeometric finite element analysis
framework. Using a manufactured solution, a mixed formulation of
the Cahn-Hilliard equation and the direct discretisation of the weak
form, which requires a C1C1-continuous approximation, are compared
in terms of convergence rates. For approximations that are higher
than second-order in space, the direct discretisation is found to
be superior. Suboptimal convergence rates occur when splines of order
p=2p=2 are used. This is validated with a priori error estimates
for linear problems. The convergence analysis is completed with an
investigation of the temporal discretisation. Second-order accuracy
is found for the generalised-? method. This ensures the functionality
of an adaptive time stepping scheme which is required for the efficient
numerical solution of the Cahn-Hilliard equation. The isogeometric
finite element framework is eventually validated by two numerical
examples of spinodal decomposition.