非正交网格上满足极值原理的扩散格式

doi:10.12286/jssx.j2020-0673

计算数学 ›› 2021, Vol. 43 ›› Issue (1): 1-16.DOI: 10.12286/jssx.j2020-0673

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非正交网格上满足极值原理的扩散格式

袁光伟

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:2020-03-10 出版日期:2021-02-15 发布日期:2021-02-04
基金资助:
国家自然科学基金（批准号：11971069）和科学挑战专题（TZ2016002）资助.

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袁光伟. 非正交网格上满足极值原理的扩散格式[J]. 计算数学, 2021, 43(1): 1-16.

Yuan Guangwei. DIFFUSION SCHEMES SATISFYING EXTREMUM PRINCIPLE ON NONORTHOGONAL MESHES[J]. Mathematica Numerica Sinica, 2021, 43(1): 1-16.

DIFFUSION SCHEMES SATISFYING EXTREMUM PRINCIPLE ON NONORTHOGONAL MESHES

Yuan Guangwei

Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, China

Received:2020-03-10 Online:2021-02-15 Published:2021-02-04

构造了非正交网格上扩散方程新的非线性单元中心型有限体积格式, 证明了该格式满足离散极值原理, 且在适当条件下具有强制性、以及在离散H¹范数下解的有界性和一阶收敛性.

关键词： 扩散方程, 非线性有限体积格式, 离散极值原理, 有界性, 收敛性

In this paper, we construct some diffusion schemes preserving extremum principle on nonorthogonal meshes. It is proved that under appropriate conditions the scheme is coercive, as well as the boundedness and first-order convergence of the discrete solution in the discrete H¹ norm.

Key words: Diffusion equations, Nonlinear finite volume schemes, Discrete extremum principle, Boundedness estimates, Convergence

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非正交网格上满足极值原理的扩散格式

DIFFUSION SCHEMES SATISFYING EXTREMUM PRINCIPLE ON NONORTHOGONAL MESHES

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