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1. High Accuracy Benchmark Problems for Allen-Cahn and Cahn-Hilliard Dynamics

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   Church, Jon M.; Guo, Zhenlin; Jimack, Peter K.; Madzvamuse, Anotida; Promislow, Keith; Wetton, Brian; Wise, Steven M.; Yang, Fengwei (October 2019, Communications in computational physics)

   There is a large literature of numerical methods for phase field models from materials science. The prototype models are the Allen-Cahn and Cahn-Hilliard equa- tions. We present four benchmark problems for these equations, with numerical results validated using several computational methods with different spatial and temporal discretizations. Our goal is to provide the scientific community with a reliable reference point for assessing the accuracy and reliability of future software for this important class of problem. 

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2. A Comparison of Cahn–Hilliard and Navier–Stokes–Cahn–Hilliard Models on Manifolds

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   Olshanskii, Maxim; Palzhanov, Yerbol; Quaini, Annalisa (May 2022, Vietnam Journal of Mathematics)
3. Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks

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   Zhao, Colby L. (July 2020, Communications in Computational Physics)

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4. Linear relaxation schemes for the Allen–Cahn-type and Cahn–Hilliard-type phase field models

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5. Allen–Cahn min-max on surfaces

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