Establishment of unified numerical methods for moving boundary problems

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When the interface between different mediums moves, the interface is called moving boundary, and the problem of tracking moving boundaries mathematically and numerically is called moving boundary problem (MBP in short). In the present research, we have studied numerical methods for MBPs, and tried to develop quite general numerical schemes and establish unified numerical methods for various MBPs. Within the research periods, we could develop quite nice unified numerical methods for curvature flow equations which are typical MBPs. Mathematical proofs such as convergence of the numerical schemes are on-going research.