@article{Lee2026, 
author = {Hyun Geun Lee},
title = {A second-order linear energy-stable scheme for slope-selection epitaxial thin-film growth},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {4},
pages = {9989-10003},
keywords = {epitaxial thin-film growth, slope selection, linear convex splitting, second-order strong-stability-preserving implicit–explicit Runge–Kutta, energy stability},
url = {https://www.sciopen.com/article/10.3934/math.2026412},
doi = {10.3934/math.2026412},
abstract = {The slope-selection epitaxial thin-film growth model was formulated as the        L    2  -gradient flow of an energy functional with a nonlinear potential of the surface slope. We developed a second-order, linear, and energy-stable scheme for this model based on a linear convex splitting in which the nonlinear potential term was treated explicitly together with an auxiliary term that ensured the convexity of the explicit part. The scheme was constructed using a second-order strong-stability-preserving implicit–explicit Runge–Kutta method. We explicitly identified the range of Runge–Kutta coefficients for which the original discrete energy decay property held, and proved that the scheme was unconditionally energy-stable with respect to the original discrete energy functional. Numerical results were presented to verify the accuracy, computational efficiency, and long-time energy stability of the scheme.}
}