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

IF 1.9 3区数学 Q2 Mathematics

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2022-04-15 DOI:10.1051/m2an/2022037

Mengjiao Jiao, Yan Jiang, Chi-Wang Shu, Mengping Zhang

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引用次数: 0

摘要

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

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.

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来源期刊

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique 数学-应用数学

CiteScore

2.70

自引率

5.30%

发文量

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.