对于MBE，无斜率选择的BDF3/EP3格式是稳定的
The BDF3/EP3 scheme for MBE with no slope selection is stable
摘要：
我们考虑经典的分子束外延（MBE）模型与对数型势称为无斜率选择。我们采用了三阶向后微分（BDF3）的时间与隐式处理的表面扩散项。非线性项近似的三阶显式外推（EP3）公式。我们表现出温和的时间步长约束下，修改后的能量耗散法持有。我们打破了第二个Dahlquist障碍，并开发了一个新的理论框架，以证明无条件的一致能量有界的时间步长没有大小的限制。这是三阶BDF方法在不引入任何稳定项或虚拟变量的情况下应用于MBE模型的第一个无条件结果。为高阶方法的误差分析建立了一个新的理论框架。
英文摘要：
We consider the classical molecular beam epitaxy (MBE) model with logarithmic type potential known as no-slope-selection. We employ a third order backward differentiation (BDF3) in time with implicit treatment of the surface diffusion term. The nonlinear term is approximated by a third order explicit extrapolation (EP3) formula. We exhibit mild time step constraints under which the modified energy dissipation law holds. We break the second Dahlquist barrier and develop a new theoretical framework to prove unconditional uniform energy boundedness with no size restrictions on the time step. This is the first unconditional result for third order BDF methods applied to the MBE models without introducing any stabilization terms or fictitious variables. A novel theoretical framework is also established for the error analysis of high order methods.
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