带坡度选择的分子束外延模型的能量稳定和收敛BDF3-5格式

IF 1.7 4区数学 Q2 MATHEMATICS, APPLIED

International Journal of Computer Mathematics Pub Date : 2023-04-26 DOI:10.1080/00207160.2023.2208236

Juan Li, Hong Sun, Xuan Zhao

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引用次数: 0

摘要

利用3-5阶后向微分公式(BDF3-5)模拟了具有坡度选择的分子束外延(MBE)模型。在估计的时间步长要求下，完全隐式的BDF3-5方案是唯一可解的。我们利用BDF3-5公式的离散梯度结构证明了这些格式保留了修正后的离散能量耗散规律。此外，我们提出了一个新的卷积不等式来处理误差估计的非线性项。更重要的是，在没有Lipschitz有界假设的情况下，严格证明了BDF3-5格式的范数收敛性分析。数值算例验证了所提方案的有效性和准确性。

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Energy stable and convergent BDF3-5 schemes for the molecular beam epitaxial model with slope selection

The backward differential formulas of order 3-5 (BDF3-5) are applied to simulate the molecular beam epitaxial (MBE) model with slop selection. The fully implicit BDF3-5 schemes are uniquely solvable under an estimated time-step requirement. We prove that the schemes conserve the modified discrete energy dissipation laws by utilizing the discrete gradient structures of BDF3-5 formulas. Furthermore, we present a new convolution inequality to handle the nonlinear term for the error estimate. More importantly, the norm convergence analysis of the BDF3-5 schemes are proved rigorously without the assumption of Lipschitz boundedness. Numerical examples are shown to verify the efficiency and the accuracy of the developed schemes.

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来源期刊

International Journal of Computer Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

5 months

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