Mesh sensitivity for numerical solutions of phase-eld equa- tions using r-adaptive nite element methods

There have been several recent works on developing moving mesh methods for solv- ing phase-eld equations. However, it is observed that some of these moving mesh solutions are essentially different with the solutions on very ne xed meshes. One of the purposes of this work 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-eld equations, the nu- merical solutions are very sensitive to the starting mesh and the monitor function. At the same time, an efcient alternating Crank-Nicolson time discretization scheme is developed for solving the nonlinear system resulting from a nite element approximation to the phase-eld equations. AMS subject classcations : 65M20, 65M50, 65M60, 80A22

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