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

被引：10

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

页码：520 / 541

页数：22

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