@Article{CiCP-29-3,
author = {Xu, Jinjing and Zhao, Fei and Zhiqiang, Sheng and Yuan, Guangwei},
title = {A Nonlinear Finite Volume Scheme Preserving Maximum Principle for Diffusion Equations},
journal = {Communications in Computational Physics},
year = {2021},
volume = {29},
number = {3},
pages = {747--766},
abstract = {<p style="text-align: justify;">In this paper we propose a new nonlinear cell-centered finite volume scheme
on general polygonal meshes for two dimensional anisotropic diffusion problems,
which preserves discrete maximum principle (DMP). The scheme is based on the so-called diamond scheme with a nonlinear treatment on its tangential flux to obtain a
local maximum principle (LMP) structure. It is well-known that existing DMP preserving diffusion schemes suffer from the fact that auxiliary unknowns should be presented as a convex combination of primary unknowns. In this paper, to get rid of
this constraint a nonlinearization strategy is introduced and it requires only a second-order accurate approximation for auxiliary unknowns. Numerical results show that
this scheme has second-order accuracy, preserves maximum and minimum for solutions and is conservative.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2020-0047},
url = {https://global-sci.com/article/79650/a-nonlinear-finite-volume-scheme-preserving-maximum-principle-for-diffusion-equations}
}