热方程全离散周期解的空间有限元和时间谱构造误差估计

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications Pub Date : 2025-01-13 DOI:10.1016/j.camwa.2025.01.008

Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao

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引用次数: 0

摘要

我们考虑了热方程周期解的全离散近似的建设性先验误差估计。我们的数值方案基于空间方向的有限元半离散化与时间方向的傅里叶展开相结合。我们推导出了最优阶显式 H1 和 L2 误差估计，这在非线性抛物方程精确解的数值验证方法中发挥了重要作用。我们还将介绍几个证实理论结果的数值示例。

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Constructive error estimates for a full-discretized periodic solution of heat equation by spatial finite-element and time spectral method

We consider the constructive a priori error estimates for a full discrete approximation of a periodic solution for the heat equation. Our numerical scheme is based on the finite element semidiscretization in space direction combined with the Fourier expansion in time. We derive the optimal order explicit H1 and L2 error estimates which play an important role in the numerical verification method of exact solutions for nonlinear parabolic equations. Several numerical examples which confirm the theoretical results will be presented.

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来源期刊

Computers & Mathematics with Applications 工程技术-计算机：跨学科应用

CiteScore

5.10

自引率

10.30%

发文量

396

审稿时长

9.9 weeks

期刊介绍： Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).