Convergence and stability of Galerkin finite element method for hyperbolic partial differential equation with piecewise continuous arguments

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Numerical Methods for Partial Differential Equations Pub Date : 2023-04-03 DOI:10.1002/num.23024

Yongtang Chen, Qi Wang

引用次数: 1

Abstract

In this paper, the convergence and stability of Galerkin finite element method for a hyperbolic partial differential equations with piecewise continuous arguments are investigated. Firstly, the variation formulation is derived by applying Green's formula and Galerkin finite element method to spatial direction of the original equation. Next, semidiscrete and fully discrete schemes are obtained and the convergence is analyzed in L2$$ {L}^2 $$ ‐norm rigorously. Moreover, the stability analysis shows that the semidiscrete scheme can achieve unconditionally stability. The sufficient conditions of stability for fully discrete scheme are also obtained under which the analytic solution is asymptotically stable. Finally, some numerical experiments are provided to demonstrate our theoretical results.

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分段连续变元双曲偏微分方程Galerkin有限元方法的收敛性和稳定性

本文研究了一类具有分段连续变元的双曲型偏微分方程的Galerkin有限元方法的收敛性和稳定性。首先，将格林公式和伽辽金有限元法应用于原方程的空间方向，导出了变分公式。接下来，得到了半离散和全离散格式，并严格分析了L2$${L}^2$$范数的收敛性。稳定性分析表明，半离散格式可以实现无条件的稳定性。给出了完全离散格式稳定性的充分条件，在此条件下解析解是渐近稳定的。最后，通过数值实验验证了我们的理论结果。

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

Numerical Methods for Partial Differential Equations 数学-应用数学

CiteScore

7.20

自引率

2.60%

发文量

审稿时长

9 months

期刊介绍： An international journal that aims to cover research into the development and analysis of new methods for the numerical solution of partial differential equations, it is intended that it be readily readable by and directed to a broad spectrum of researchers into numerical methods for partial differential equations throughout science and engineering. The numerical methods and techniques themselves are emphasized rather than the specific applications. The Journal seeks to be interdisciplinary, while retaining the common thread of applied numerical analysis.