Pin-pointing the phase boundary with the mesh transformation method in a relaxed double-well problem

摘要

The mesh transformation method (MTM), which redistributes the mesh in favor of energy minimization, is applied to numerically solving a l-dimensional relaxed double-well phase transition model problem. In piece-wise affine continuous finite element function spaces with N mesh nodes, the convergence rate of the numerical solution is shown to be O(N~(-1)) in H~1-norm. The MTM solutions are shown to preserve some important prop-erties of the problem. In particular, with MTM, the phase boundary, which separates the regions with or without undergoing austenitic-martensitic phase transition and is considered one of the most important physical features in the macroscopic phase transition model, is shown to be pin-pointed with an accuracy of order O(N~(-2)).