Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich-Schwoebel Type Energy: Application to Thin Film Epitaxy

By Jie Shen, Cheng Wang, Xiaoming Wang, Steven M. Wise. SIAM Journal on Numerical Analysis, 2012

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Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks (2020, background): “Here is some literature that attracts our attention [9, 10, 16, 26, 27, 30, 31].”
A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows (2017, unknown): “While it is possible to construct second-order convex splitting schemes for certain situations on a case by case basis (see, for instance, [67, 10, 72]), a general formulation of second-order convex splitting schemes is not available.”
A Second-Order Energy Stable BDF Numerical Scheme for the Cahn-Hilliard Equation (2018, background): “See the related works for the phase field crystal (PFC) equation and the modified phase field crystal (MPFC) equation [3, 4, 28, 35, 37]; epitaxial thin film growth models [8, 10, 32, 34]; non-local Cahn-Hilliard-type models [22, 23]; the CHHS and related models [9, 13, 20, 36]; et cetera.”
A novel linear second order unconditionally energy stable scheme for a hydrodynamic Q-tensor model of liquid crystals (2017, methodology): “About the standard analysis technique when the space discretization is involved, we refer to [35,33].”
Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method (2017, background): “[3, 10, 27, 37]), where the convex part of the potential is treated implicitly while the concave part is treated explicitly.”