Mesh Sensitivity for Numerical Solutions of Phase-Field Equations Using r-Adaptive Finite Element Methods (Communications in Computational Physics, 2018)
There have been several recent papers on developing moving mesh methodsfor solving phase-field equations. However, it is observed that some of these movingmesh 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. Wecarried 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 tothe starting mesh and the monitor function. As a separate issue, an efficient alternating Crank-Nicolson time discretization scheme is developed for solving the nonlinearsystem resulting from a finite element approximation to the phase-field equations.