Error estimate of high order Runge–Kutta local discontinuous Galerkin method for nonlinear convection-dominated Sobolev equation

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED Journal of Computational and Applied Mathematics Pub Date : 2025-03-31 DOI:10.1016/j.cam.2025.116657

Caiyue Du , Di Zhao , Qiang Zhang

引用次数: 0

Abstract

In this paper we consider an efficient fully-discrete scheme for solving the nonlinear convection-dominated Sobolev equation, which adopts the local discontinuous Galerkin method with generalized numerical fluxes and high order explicit Runge–Kutta time-marching. By the generalized Gauss-Radau projection and the matrix transferring process, we obtain the optimal

L^{2}

-norm error estimate in both space and time. It is worth mentioning that the bounding constant in error estimate is independent of the reciprocals of diffusion and dispersion coefficients. Finally, numerical experiments are presented to support theoretical results.

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非线性对流主导Sobolev方程的高阶龙格-库塔局部不连续Galerkin方法误差估计

本文考虑了求解非线性对流主导Sobolev方程的一种有效的全离散格式，该格式采用具有广义数值通量和高阶显式龙格-库塔时间推进的局部不连续Galerkin方法。通过广义高斯-拉道投影和矩阵变换，得到了空间和时间上最优的l2范数误差估计。值得一提的是，误差估计中的边界常数与扩散系数和色散系数的倒数无关。最后，通过数值实验验证了理论结果。

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

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.

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