Abstract
The epitaxial thin film growth model without slope selection is the L2-gradient flow of energy with a logarithmic potential in terms of the gradient of a height function. A challenge to numerically solving the model is how to treat the nonlinear term to preserve energy stability without compromising accuracy and efficiency. To resolve this problem, we present a high-order energy stable scheme by placing the linear and nonlinear terms in the convex and concave parts, respectively, and employing the specially designed implicit–explicit Runge–Kutta method. As a result, our scheme is linear, high-order accurate in time, and unconditionally energy stable. We show analytically that the scheme is unconditionally uniquely solvable and energy stable. Numerical experiments are presented to demonstrate the accuracy, efficiency, and energy stability of the proposed scheme.
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