Abstract In this paper, we propose a finite volume scheme preserving discrete maximum principle (DMP) for the imperfect interface problem. We prove the existence of the numerical solution and prove that when the interface parameter tends to 0, the numerical solutions of imperfect interface problem have a subsequence converging to the numerical solution of perfect interface problem. We apply a domain decomposition method called Robin-Robin iteration to solve the scheme and prove the DMP on each iteration step. The numerical experiments show the DMP-preserving property and accuracy of this scheme.

中文翻译：

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非完美界面扩散方程的一种保留最大值原理的有限体积法

摘要 在本文中，我们针对不完美界面问题提出了一种保留离散最大值原理（DMP）的有限体积方案。我们证明了数值解的存在性，并证明了当界面参数趋于0时，非完美界面问题的数值解有一个收敛于完美界面问题的数值解的子序列。我们应用称为 Robin-Robin 迭代的域分解方法来求解该方案并在每个迭代步骤中证明 DMP。数值实验表明了该方案的 DMP 保留特性和准确性。