@Article{CiCP-32-5,
author = {Li, Ang and Yang, Hongtao and Yonghai, Li and Yuan, Guangwei},
title = {The Corrected Finite Volume Element Methods for Diffusion Equations Satisfying Discrete Extremum Principle},
journal = {Communications in Computational Physics},
year = {2022},
volume = {32},
number = {5},
pages = {1437--1473},
abstract = {<p style="text-align: justify;">In this paper, we correct the finite volume element methods for diffusion
equations on general triangular and quadrilateral meshes. First, we decompose the
numerical fluxes of original schemes into two parts, i.e., the principal part with a two-point flux structure and the defective part. And then with the help of local extremums,
we transform the original numerical fluxes into nonlinear numerical fluxes, which can
be expressed as a nonlinear combination of two-point fluxes. It is proved that the
corrected schemes satisfy the discrete strong extremum principle without restrictions
on the diffusion coefficient and meshes. Numerical results indicate that the corrected
schemes not only satisfy the discrete strong extremum principle but also preserve the
convergence order of the original finite volume element methods.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2022-0130},
url = {https://global-sci.com/article/79502/the-corrected-finite-volume-element-methods-for-diffusion-equations-satisfying-discrete-extremum-principle}
}