Physical-bound-preserving finite volume methods for the Nagumo equation on distorted meshes

作者：Zhou, Huifang; Sheng, Zhiqiang; Yuan, Guangwei^*

来源：Computers & Mathematics with Applications, 2019, 77(4): 1055-1070.

DOI：10.1016/j.camwa.2018.10.038

• Boundedness
• Finite volume
• Nagumo equation
• Distorted meshes

In this paper, we present a boundedness preserving finite volume scheme for the Nagumo equation. In this method, we use the implicit Euler method for the time discretization, and construct a maximum-principle-preserving discrete normal flux for the diffusion term. For the nonlinear reaction term, we design a type of Picard iteration to ensure that at each iterative step it keeps physical boundedness. Moreover we prove that the numerical solution of the resulting scheme can preserve the bound of the solution for the Nagumo equation on distorted meshes. Some numerical results are presented to verify the theoretical analysis.

• 出版日期2019-2-15
• 单位北京应用物理与计算数学研究所; 中国工程物理研究院