This report presents the time filtered BDF- (FiBDF-) methods up to fourth-order time accuracy for the molecular beam epitaxial equation with no-slope selection. The new -order methods are developed by introducing an inexpensive post-filtering step to the variable-step BDF- methods. We show that the FiBDF- methods are uniquely solvable and volume conservative. Some novel discrete gradient structures of the FiBDF- formulas are derived such that we can build up the discrete energy dissipation laws for the associated time-steppings. Numerical examples are included to show the mesh-robustness and effectiveness of the variable-step methods especially in the long-time simulations.

中文翻译：

---

分子束外延方程的时间滤波 BDF 方法高达四阶的能量耗散定律

本报告介绍了无斜率选择的分子束外延方程的时间滤波 BDF- (FiBDF-) 方法，其时间精度高达四阶。新阶方法是通过向可变步长 BDF 方法引入廉价的后滤波步骤而开发的。我们证明 FiBDF 方法具有独特的可解性和体积保守性。导出了 FiBDF 公式的一些新颖的离散梯度结构，以便我们可以为相关的时间步长建立离散能量耗散定律。数值例子显示了变步长方法的网格鲁棒性和有效性，特别是在长时间模拟中。