OPTIMAL ERROR ESTIMATES OF THE SEMIDISCRETE CENTRAL DISCONTINUOUS GALERKIN METHODS FOR LINEAR HYPERBOLIC EQUATIONS

被引：11
|
作者：
Liu, Yong [1 ]
Shu, Chi-Wang [2 ]
Zhang, Mengping [1 ]
机构：
[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China
[2] Brown Univ, Div Appl Math, Providence, RI 02912 USA
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2018年 / 56卷 / 01期
基金：
美国国家科学基金会;
关键词：
optimal error estimate; central DG; superconvergence points; CONSERVATION-LAWS; OVERLAPPING CELLS; DIFFUSION-EQUATIONS; CENTRAL SCHEMES; STABILITY; SUPERCONVERGENCE;
D O I：
10.1137/16M1089484
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We analyze the central discontinuous Galerkin method for time-dependent linear conservation laws. In one dimension, optimal a priori L-2 error estimates of order k + 1 are obtained for the semidiscrete scheme when piecewise polynomials of degree at most k (k >= 0) are used on overlapping uniform meshes. We then extend the analysis to multidimensions on uniform Cartesian meshes when piecewise tensor-product polynomials are used on overlapping meshes. Numerical experiments are given to demonstrate the theoretical results.
引用
收藏
页码：520 / 541
页数：22
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