On the superconvergence of a WG method for the elliptic problem with variable coefficients  

作　　者：Junping Wang Xiaoshen Wang Xiu Ye Shangyou Zhang Peng Zhu 

机构地区：[1]Division of Mathematical Sciences,National Science Foundation,Alexandria,VA 22314,USA [2]Department of Mathematics,University of Arkansas at Little Rock,Little Rock,AR 72204,USA [3]Department of Mathematical Sciences,University of Delaware,Newark,DE 19716,USA [4]College of Data Science,Jiaxing University,Jiaxing 314001,China

出　　处：《Science China Mathematics》2024年第8期1899-1910,共12页中国科学（数学）（英文版）

基　　金：supported by U.S.National Science Foundation IR/D program while working at U.S.National Science Foundation;supported by U.S.National Science Foundation(Grant No.DMS-1620016);supported by Zhejiang Provincial Natural Science Foundation of China(Grant No.LY23A010005);National Natural Science Foundation of China(Grant No.12071184)。

摘　　要：This article extends a recently developed superconvergence result for weak Galerkin(WG)approximations for modeling partial differential equations from constant coefficients to variable coefficients.This superconvergence features a rate that is two orders higher than the optimal-order error estimates in the usual energy and L^(2)norms.The extension from constant to variable coefficients for the modeling equations is highly non-trivial.The underlying technical analysis is based on a sequence of projections and decompositions.Numerical results confirm the superconvergence theory for second-order elliptic problems with variable coefficients.

关 键 词：weak Galerkin finite element methods SUPERCONVERGENCE second-order elliptic problems stabilizerfree 

分 类 号：O241.82[理学—计算数学]