New approximate method for the Allen–Cahn equation with double-obstacle constraint and stability criteria for numerical simulations
نویسندگان
چکیده
Abstract: 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 subdifferential of the indicator function on a closed interval. Therefore, performing a numerical simulation of our problem poses difficulties. 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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تاریخ انتشار 2016