Bound preserving and energy dissipative schemes for porous medium equation
Bound preserving and energy dissipative schemes for porous medium equation
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DOI：
10.1016/j.jcp.2020.109378
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发表时间：
2020-06
期刊：
影响因子：
--
通讯作者：
Yiqi Gu;Jie Shen
中科院分区：
文献类型：
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作者：
Yiqi Gu;Jie Shen
本文构造了一类多孔介质方程的保界耗能格式。这些格式基于Wasserstein梯度流的正性保持方法和摄动技术，并且被证明是唯一可解的、保界的，并且在一阶情况下也是能量耗散的。文中给出了大量的数值结果，验证了理论结果和新格式的有效性。
A class of bound preserving and energy dissipative schemes for the porous medium equation are constructed in this paper. The schemes are based on a positivity preserving approach for Wasserstein gradient flow and a perturbation technique, and are shown to be uniquely solvable, bound preserving, and in the first-order case, also energy dissipative. Ample numerical results are presented to validate the theoretical results and demonstrate the effectiveness of the new schemes.