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

被引：1

作者：

Wang, Junping ^{[1
]}

Wang, Xiaoshen ^{[2
]}

Ye, Xiu ^{[2
]}

Zhang, Shangyou ^{[3
]}

Zhu, Peng ^{[4
]}

机构：

[1] Natl Sci Fdn, Div Math Sci, Alexandria, VA 22314 USA

[2] Univ Arkansas Little Rock, Dept Math, Little Rock, AR 72204 USA

[3] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

[4] Jiaxing Univ, Coll Data Sci, Jiaxing 314001, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2024年 / 67卷 / 08期

基金：

美国国家科学基金会; 中国国家自然科学基金;

关键词：

weak Galerkin finite element methods; superconvergence; second-order elliptic problems; stabilizer-free; FINITE-ELEMENT-METHOD; WEAK GALERKIN METHOD;

D O I：

10.1007/s11425-022-2097-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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-order higher than the optimal-order error estimates in the usual energy and L2 norms. The extension from constant to variable coefficients for the modeling equations is highly non-trivial. The underlying technical analysis is based on the use of a sequence of projections and decompositions. Numerical results are presented to confirm the superconvergence theory for second-order elliptic problems with variable coefficients.

引用

页码：1899 / 1910

页数：12

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