Discrete Maximal Regularity for the Discontinuous Galerkin Time-Stepping Method without Logarithmic Factor

IF 2.8 2区 数学 Q1 MATHEMATICS, APPLIED
Takahito Kashiwabara, Tomoya Kemmochi
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引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 1638-1659, August 2024.
Abstract. Maximal regularity is a kind of a priori estimate for parabolic-type equations, and it plays an important role in the theory of nonlinear differential equations. The aim of this paper is to investigate the temporally discrete counterpart of maximal regularity for the discontinuous Galerkin (DG) time-stepping method. We will establish such an estimate without logarithmic factor over a quasi-uniform temporal mesh. To show the main result, we introduce the temporally regularized Green’s function and then reduce the discrete maximal regularity to a weighted error estimate for its DG approximation. Our results would be useful for investigation of DG approximation of nonlinear parabolic problems.
无对数因子的非连续伽勒金时间步进方法的离散最大正则性
SIAM 数值分析期刊》第 62 卷第 4 期第 1638-1659 页,2024 年 8 月。 摘要最大正则性是抛物型方程的一种先验估计,在非线性微分方程理论中占有重要地位。本文旨在研究非连续伽勒金(DG)时步法的最大正则性的时间离散对应关系。我们将在准均匀时间网格上建立这种不含对数因子的估计。为了说明主要结果,我们引入了时间正则化的格林函数,然后将离散最大正则性简化为其 DG 近似的加权误差估计。我们的结果将有助于研究非线性抛物问题的 DG 近似。
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
CiteScore
4.80
自引率
6.90%
发文量
110
审稿时长
4-8 weeks
期刊介绍: SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.
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