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