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New approximate method for the Allen–Cahn equation with double-obstacle constraint and stability criteria for numerical simulations

Tomoyuki Suzuki Keisuke Takasao Noriaki Yamazaki

*Corresponding author: Noriaki Yamazaki noriaki@kanagawa-u.ac.jp

Math2016,3,288doi:10.3934/Math.2016.3.288

In a numerical study, we consider the Allen–Cahn equation with a double-obstacle constraint. The constraint is a multivalued function that is provided by the subdi erential of the indicator function on a closed interval. Therefore, performing a numerical simulation of our problem poses diffculties. We propose a new approximate method for the constraint and demonstrate its validity. Moreover, we present stability criteria for the standard forward Euler method guaranteeing stable numerical experiments when using the approximating equation.

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