发表机构
University of Stuttgart; Université de Strasbourg（斯图加特大学; 斯特拉斯堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种用于四阶PDE双曲逼近的保结构IMEX方法，证明其能量一致、保正且渐近稳定，并通过薄膜方程算例验证有效性。
AI 中文摘要
我们针对一阶双曲逼近系统提出了一种新颖的保结构数值方法，该系统用于逼近一般四阶偏微分方程的解。通过采用刚性项与非刚性项之间的隐式-显式（IMEX）分裂，我们严格证明了所提格式在CFL型条件下具有能量一致性和正性保持性质。此外，我们表明该方法在渐近区域中保持稳健稳定，其时间步长限制完全独立于松弛参数。最后，我们针对薄膜方程展示了一系列数值算例，以验证该格式的理论性质与有效性。
英文摘要
We introduce a novel structure-preserving numerical method for a first-order hyperbolic approximation system, which approximates the solutions of general fourth-order partial differential equations. By employing an implicit-explicit (IMEX) splitting between the stiff and non-stiff terms, we rigorously prove that the proposed scheme is energy-consistent and positivity-preserving under a CFL-type condition. Furthermore, we show that the method remains robustly stable in asymptotic regimes, with a time-step restriction that is entirely independent of the relaxation parameters. Finally, we present a series of numerical examples for thin film equations to validate the theoretical properties and efficacy of the scheme.
