Analysis of a p-version finite volume method for 1D elliptic problems

被引：0
作者：
Cao, Waixiang [1 ]
Zhang, Zhimin [1 ,2 ]
Zou, Qingsong [3 ,4 ]
机构：
[1] Beijing Computat Sci Res Ctr, Beijing 100084, Peoples R China
[2] Wayne State Univ, Dept Math, Detroit, MI 48202 USA
[3] Sun Yat Sen Univ, Coll Math & Sci Comp, Guangzhou 510275, Guangdong, Peoples R China
[4] Sun Yat Sen Univ, Guangdong Prov Key Lab Computat Sci, Guangzhou 510275, Guangdong, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2014年 / 265卷
基金：
美国国家科学基金会; 中国国家自然科学基金;
关键词：
p-version; Superconvergence; Finite volume method; ELEMENT-METHOD; SUPERCONVERGENCE;
D O I：
10.1016/j.cam.2013.09.044
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work, we present and analyze a p-version finite volume method (RIM) for elliptic problems in the one dimensional setting. Under some regularity assumptions of the exact solution, it is shown that the p-version FV solution converges with exponential rates under H-1, L-2 and L-oe-norms. Superconvergence properties at nodal, Lobatto and Gauss points have been also discussed. Numerical results are presented to support our theoretical findings. (c) 2013 Elsevier B.V. All rights reserved.
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页码：17 / 32
页数：16
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