Optimal error estimates to smooth solutions of the central discontinuous Galerkin methods for nonlinear scalar conservation laws

IF 1.9 3区 数学 Q2 Mathematics
Mengjiao Jiao, Yan Jiang, Chi-Wang Shu, Mengping Zhang
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引用次数: 0

Abstract

In this paper, we study the error estimates to sufficiently smooth solutions of the nonlinear scalar conservation laws for the semi-discrete central discontinuous Galerkin (DG) nite element methods on uniform Cartesian meshes. A general approach with an explicitly checkable condition is established for the proof of optimal L2 error estimates of the semi-discrete CDG schemes, and this condition is checked to be valid in one and two dimensions for polynomials of degree up to k = 8. Numerical experiments are given to verify the theoretical results.
非线性标量守恒律中心不连续伽辽金方法光滑解的最优误差估计
本文研究了均匀笛卡尔网格上半离散中心不连续伽辽金(DG)有限元法非线性标量守恒律充分光滑解的误差估计。建立了半离散CDG格式的最优L2误差估计的一般证明方法,该方法具有显式可检验条件,并对k = 8次多项式在一维和二维上的有效性进行了检验。数值实验验证了理论结果。
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来源期刊
CiteScore
2.70
自引率
5.30%
发文量
27
审稿时长
6-12 weeks
期刊介绍: M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.
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