A local discontinuous Galerkin methods with local Lax-Friedrichs flux and modified central flux for one dimensional nonlinear convection-diffusion equation

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED Applied Numerical Mathematics Pub Date : 2024-11-15 DOI:10.1016/j.apnum.2024.11.009

Jia Li , Wei Guan , Shengzhu Shi , Boying Wu

引用次数: 0

Abstract

In this paper, we study the local discontinuous Galerkin (LDG) method for one-dimensional nonlinear convection-diffusion equation. In the LDG scheme, local Lax-Friedrichs numerical flux is adopted for the convection term, and a modified central flux is proposed and applied to the nonlinear diffusion coefficient. The modified central flux overcomes the shortcomings of the traditional flux, and it is beneficial in proving the

L^{2}

stability of the LDG scheme. By virtue of the Gauss-Radau projections and the local linearization technique, the optimal error estimates are also obtained. Numerical experiments are presented to confirm the validity of the theoretical results.

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针对一维非线性对流扩散方程的局部非连续伽勒金方法与局部 Lax-Friedrichs 通量和修正的中心通量

本文研究了一维非线性对流扩散方程的局部非连续伽勒金（LDG）方法。在 LDG 方案中，对流项采用局部 Lax-Friedrichs 数值通量，并提出了一种修正的中心通量，将其应用于非线性扩散系数。修正的中心通量克服了传统通量的缺点，有利于证明 LDG 方案的 L2 稳定性。通过高斯-拉道投影和局部线性化技术，还获得了最优误差估计。数值实验证实了理论结果的正确性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.