A finite volume method preserving maximum principle for the diffusion equations with imperfect interface

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.