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 superconvergen...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.展开更多
基金supported by U.S.National Science Foundation IR/D program while working at U.S.National Science Foundationsupported by U.S.National Science Foundation(Grant No.DMS-1620016)+1 种基金supported by Zhejiang Provincial Natural Science Foundation of China(Grant No.LY23A010005)National Natural Science Foundation of China(Grant No.12071184)。
文摘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.
