A stable and structure-preserving scheme for a non-local Allen-Cahn equation. (English) Zbl 1403.65043
Summary: We propose a stable and structure-preserving finite difference scheme for a non-local Allen-Cahn equation which describes a process of phase separation in a binary mixture. The proposed scheme inherits characteristic properties, the conservation of mass and the decrease of the global energy from the equation. We show the stability and unique existence of the solution of the scheme. We also prove the error estimate for the scheme. Numerical experiments demonstrate the effectiveness of the proposed scheme.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
References:
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