June 1, 2024Advances in Applied Mathematics and MechanicsOpen Access

A Linear Doubly Stabilized Crank-Nicolson Scheme for the Allen–Cahn Equation with a General Mobility

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Unconditional preservation of the maximum bound principle is achieved for the Allen-Cahn equation using mild parameter restrictions, ensuring uniform solution boundedness.
Temporal discretization using the Crank-Nicolson formula and spatial approximation via the central finite difference method establish a linear fully discrete numerical scheme.
Supports robust phase-field simulations through verified energy stability, while derived error estimates provide optimal convergence bounds for variable mobility models.

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Implication

Assessment of a linear Crank-Nicolson scheme demonstrates unconditional maximum bound principle preservation for the Allen-Cahn equation, indicating guaranteed energy stability.

Cite This Study

Hou et al. (2024) studied this question.

synapsesocial.com/papers/68e66b13b6db6435875f6246 https://doi.org/10.4208/aamm.oa-2023-0067

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Implication

Assessment of a linear Crank-Nicolson scheme demonstrates unconditional maximum bound principle preservation for the Allen-Cahn equation, indicating guaranteed energy stability.

A Linear Doubly Stabilized Crank-Nicolson Scheme for the Allen–Cahn Equation with a General Mobility

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Discussion

Implication

Cite This Study

A Linear Doubly Stabilized Crank-Nicolson Scheme for the Allen–Cahn Equation with a General Mobility

Key Points

Discussion

Implication

Cite This Study

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