New Superconvergent Structures with Optional Superconvergent Points for the Finite Volume Element Method  

作　　者：XiangWang Yuqing Zhang Zhimin Zhang 

机构地区：[1]School of Mathematics,Jilin University,Changchun 130012,China [2]Department of Mathematics,Wayne State University,Detroit,MI 48202,USA

出　　处：《Communications in Computational Physics》2023年第5期1332-1356,共25页计算物理通讯（英文）

基　　金：This work is supported in part by the National Natural Science Foundation of China under grants 11701211,11871092,12131005;the China Postdoctoral Science Foundation under grant 2021M690437。

摘　　要：New superconvergent structures are proposed and analyzed for the finite volume element(FVE)method over tensorial meshes in general dimension d(for d≥2);we call these orthogonal superconvergent structures.In this framework,one has the freedom to choose the superconvergent points of tensorial k-order FVE schemes(for k≥3).This flexibility contrasts with the superconvergent points(such as Gauss points and Lobatto points)for current FE schemes and FVE schemes,which are fixed.The orthogonality condition and the modified M-decomposition(MMD)technique that are developed over tensorial meshes help in the construction of proper superclose functions for the FVE solutions and in ensuring the new superconvergence properties of the FVE schemes.Numerical experiments are provided to validate our theoretical results.

关 键 词：SUPERCONVERGENCE finite volume orthogonality condition tensorial mesh rectangular mesh 

分 类 号：O241.82[理学—计算数学]