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

Science China Mathematics 2023年第4期66卷 855-886页

作者： Peng Yang Xiang Wang Yonghai Li School of Mathematics Jilin UniversityChangchun 130012China BNU-UIC Research Center for Mathematics Beijing Normal UniversityZhuhai 519087China

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.

关键词： finite volume method tetrahedral mesh orthogonal condition minimum V-angle condition stability and convergence

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On the Construction and Analysis of Finite Volume Element Schemes with Optimal L^(2) Convergence Rate

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Numerical Mathematics(Theory,Methods and Applications) 2021年第1期14卷 47-70页

作者： Xiang Wang Yuqing Zhang School of Mathematics Jilin UniversityChangchun 130012China

We provide a general construction method for a finite volume element(FVE)scheme with the optimal L^(2)convergence *** k-(k-1)-order orthogonal condition(generalized)is proved to be a sufficient and necessary condition for a k-order FVE scheme to have the optimal L^(2) convergence rate in 1D,in which the independent dual parameters constitute a(k-1)-dimension surface in the reasonable domain in *** the analysis,the dual strategies in different primary elements are not necessarily to be the same,and they are allowed to be asymmetric in each primary element,which open up more possibilities of the FVE schemes to be applied to some complex problems,such as the convection-dominated *** worth mentioning that,the construction can be extended to the quadrilateral meshes in *** stability and H^(1) estimate are proved for *** the above results are demon-strated by numerical experiments.

关键词： Finite volume L^(2)estimate sufficient and necessary condition orthogonal condition

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