The Allen-Cahn equation has been widely used to model various phenomena in nature. In particular it has become a basic model equation for the diffuse interface approach developed to study phase transitions and interfacial dynamics in materials science. As the exact solutions of the Allen-Cahn equation cannot be found, numerical methods have played an important role in various simulations. One of the important numerical aspects is about the discrete stability of the numerical schemes. This project is to carry out a systematic study on the numerical stability for the numerical solutions to the Allen-Cahn equation. The numerical approximations will involve finite difference, finite element and spectral method in space and implicit-explicit scheme in time. The goal is to identify some effective numerical schemes that provide high resolution in space and allow reasonably large time steps in time.
|Effective start/end date
|1/09/14 → 31/08/17
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