Construction and analysis of the quadratic finite volume methods on tetrahedral meshes

作     者：Peng Yang Xiang Wang Yonghai Li 

作者机构：School of MathematicsJilin UniversityChangchun 130012China BNU-UIC Research Center for MathematicsBeijing Normal UniversityZhuhai 519087China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2023年第66卷第4期

页      面：855-886页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant Nos.12071177 and 11701211) the Science Challenge Project(Grant No.TZ2016002) the China Postdoctoral Science Foundation(Grant No.2021M690437) 

主　　题：finite volume method tetrahedral mesh orthogonal condition minimum V-angle condition stability and convergence 

摘      要：We construct and analyze a family of quadratic finite volume method(FVM)schemes over tetrahedral *** order to prove the stability and the error estimate,we propose the minimum V-angle condition on tetrahedral meshes,and the surface and volume orthogonal conditions on dual *** the technique of element analysis,the local stability is equivalent to a positive definiteness of a 9 × 9 element matrix,which is difficult to analyze directly or even *** the help of the surface orthogonal condition and the congruent transformation,this element matrix is reduced into a block diagonal matrix,and then we carry out the stability result under the minimum V-angle *** is worth mentioning that the minimum V-angle condition of the tetrahedral case is very different from a simple extension of the minimum angle condition for triangular meshes,while it is also convenient to use in *** on the stability,we prove the optimal H^(1) and L^(2) error estimates,respectively,where the orthogonal conditions play an important role in ensuring the optimal L^(2) convergence *** experiments are presented to illustrate our theoretical results.