An Arbitrary-Order Discontinuous Galerkin Method with One Unknown Per Element

被引：30
作者：
Li, Ruo [1 ,2 ]
Ming, Pingbing [3 ,4 ]
Sun, Ziyuan [2 ]
Yang, Zhijian [5 ]
机构：
[1] Peking Univ, LMAM, CAPT, Beijing 100871, Peoples R China
[2] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
[3] Chinese Acad Sci, Acad Math & Syst Sci, LSEC, 55 Zhong Guan Cun East Rd, Beijing 100190, Peoples R China
[4] Univ Chinese Acad Sci, Sch Math Sci, 19A Yu Quan Rd, Beijing 100049, Peoples R China
[5] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China
来源：
JOURNAL OF SCIENTIFIC COMPUTING | 2019年 / 80卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Least-squares reconstruction; Discontinuous Galerkin method; Elliptic problem;
D O I：
10.1007/s10915-019-00937-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We propose an arbitrary-order discontinuous Galerkin method for second-order elliptic problem on general polygonal mesh with only one degree of freedom per element. This is achieved by locally solving a discrete least-squares over a neighboring element patch. Under a geometrical condition on the element patch, we prove an optimal a priori error estimates in the energy norm and in the L2 norm. The accuracy and the efficiency of the method up to order six on several polygonal meshes are illustrated by a set of benchmark problems.
引用
收藏
页码：268 / 288
页数：21
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