• 论文 •

扩散方程九点格式的保正性与极值性

1. 北京应用物理与计算数学研究所, 北京8009信箱, 北京 100094
• 收稿日期:2020-02-29 出版日期:2021-06-15 发布日期:2021-06-03
• 基金资助:
国家自然科学基金（批准号：11971069）与科学挑战专题（TZ2016002）资助.

Yuan Guangwei. POSITIVITY AND EXTREMUM PRESERVING OF NINE POINT SCHEMES FOR DIFFUSION EQUATIONS[J]. Journal on Numerica Methods and Computer Applications, 2021, 42(2): 134-145.

POSITIVITY AND EXTREMUM PRESERVING OF NINE POINT SCHEMES FOR DIFFUSION EQUATIONS

Yuan Guangwei

1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
• Received:2020-02-29 Online:2021-06-15 Published:2021-06-03

For the existing nine point scheme for diffusion equation on arbitrary quadrilateral meshes, a suitable limiter is introduced to modify discrete flux. It is proved that the obtained nonlinear scheme has strong positivity-preserving property, and the solution (if there exists one) of the nonlinear scheme is just a positive solution of the nine point scheme. Furthermore, the scheme of preserving discrete strong extremum principle is investigated.

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