ANALYSIS OF TWO ANY ORDER SPECTRAL VOLUME METHODS FOR 1-D LINEAR HYPERBOLIC EQUATIONS WITH DEGENERATE VARIABLE COEFFICIENTS  

作　　者：Minqiang Xu Yanting Yuan Waixiang Cao Qingsong Zou 

机构地区：[1]College of Science,Zhejiang University of Technology,Hangzhou 310023,China [2]School of Computer Science and Engineering,Sun Yat-sen University,Guangzhou 510275,China [3]School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China [4]School of Computer Science and Engineering,and Guangdong Province Key Laboratory of Computational Science,Sun Yat-sen University,Guangzhou 510275,China

出　　处：《Journal of Computational Mathematics》2024年第6期1627-1655,共29页计算数学（英文）

基　　金：supported by the NSFC(Grants 92370113,12071496,12271482);Moreover,the first author was also supported by the Zhejiang Provincial NSF(Grant LZ23A010006);by the Key Research Project of Zhejiang Lab(Grant 2022PE0AC01);the fourth author was also supported by the Guangdong Provincial NSF(Grant 2023A1515012097).

摘　　要：In this paper,we analyze two classes of spectral volume(SV)methods for one-dimensional hyperbolic equations with degenerate variable coefficients.Two classes of SV methods are constructed by letting a piecewise k-th order(k≥1 is an integer)polynomial to satisfy the conservation law in each control volume,which is obtained by refining spectral volumes(SV)of the underlying mesh with k Gauss-Legendre points(LSV)or Radaus points(RSV)in each SV.The L^(2)-norm stability and optimal order convergence properties for both methods are rigorously proved for general non-uniform meshes.Surprisingly,we discover some very interesting superconvergence phenomena:At some special points,the SV flux function approximates the exact flux with(k+2)-th order and the SV solution itself approximates the exact solution with(k+3/2)-th order,some superconvergence behaviors for element averages errors have been also discovered.Moreover,these superconvergence phenomena are rigorously proved by using the so-called correction function method.Our theoretical findings are verified by several numerical experiments.

关 键 词：Spectral Volume Methods L^(2)stability Error estimates SUPERCONVERGENCE 

分 类 号：O17[理学—数学]