@Article{AAMM-15-4,
author = {Wu, Dan and Lv, Junliang and Lin, Lei and Zhiqiang, Sheng},
title = {A Maximum-Principle-Preserving Finite Volume Scheme for Diffusion Problems on Distorted Meshes},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2023},
volume = {15},
number = {4},
pages = {1076--1108},
abstract = {<p style="text-align: justify;">In this paper, we propose an approach for constructing conservative and
maximum-principle-preserving finite volume schemes by using the method of undetermined coefficients, which depend nonlinearly on the linear non-conservative one-sided fluxes. In order to facilitate the derivation of expressions of these undetermined
coefficients, we explicitly provide a simple constriction condition with a scaling parameter. Such constriction conditions can ensure the final schemes are exact for linear
solution problems and may induce various schemes by choosing different values for
the parameter. In particular, when this parameter is taken to be 0, the nonlinear terms
in our scheme degenerate to a harmonic average combination of the discrete linear
fluxes, which has often been used in a variety of maximum-principle-preserving finite
volume schemes. Thus our method of determining the coefficients of the nonlinear
terms is more general. In addition, we prove the convergence of the proposed schemes
by using a compactness technique. Numerical results demonstrate that our schemes
can preserve the conservation property, satisfy the discrete maximum principle, possess a second-order accuracy, be exact for linear solution problems, and be available
for anisotropic problems on distorted meshes.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2022-0224},
url = {https://global-sci.com/article/72866/a-maximum-principle-preserving-finite-volume-scheme-for-diffusion-problems-on-distorted-meshes}
}