The Corrected Finite Volume Element Methods for Diffusion Equations Satisfying Discrete Extremum Principle

作     者：Ang Li Hongtao Yang Yonghai Li Guangwei Yuan 

作者机构：School of MathematicsJilin UniversityChangchun 130012JilinChina Institute of Applied Physics and Computational MathematicsFenghaodong RoadHaidian DistrictBeijing 100094China 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2022年第32卷第10期

页      面：1437-1473页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学] 

基　　金：partially supported by the National Science Foundation of China(No.12071177,No.12126307,No.11971069) the Science Challenge Project(No.TZ2016002) 

主　　题：Diffusion equations finite volume element flux-correct maximum principle 

摘      要：In this paper,we correct the finite volume element methods for diffusion equations on general triangular and quadrilateral ***,we decompose the numerical fluxes of original schemes into two parts,i.e.,the principal part with a twopoint flux structure and the defective *** 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 *** is proved that the corrected schemes satisfy the discrete strong extremum principle without restrictions on the diffusion coefficient and *** 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.