TY - JOUR
T1 - Mesh Sensitivity for Numerical Solutions of Phase-Field Equations Using r-Adaptive Finite Element Methods
JO - Communications in Computational Physics
VL - 2
SP - 357
EP - 375
PY - 2008
DA - 2008/03
SN - 3
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cicp/7858.html
KW - 
AB - <p style="text-align: justify;">There have been several recent papers on developing moving mesh methods
for solving phase-field equations. However, it is observed that some of these moving
mesh solutions are essentially different from the solutions on very fine fixed meshes.
One of the purposes of this paper is to understand the reason for the differences. We
carried out numerical sensitivity studies systematically in this paper and it can be concluded that for the phase-field equations, the numerical solutions are very sensitive to
the starting mesh and the monitor function. As a separate issue, an efficient alternating Crank-Nicolson time discretization scheme is developed for solving the nonlinear
system resulting from a finite element approximation to the phase-field equations.</p>