A posteriori error estimates for Radau IIA methods via maximal parabolic regularity

Akrivis Georgios; Makridakis Charalambos G.

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A posteriori error estimates for Radau IIA methods via maximal parabolic regularity

机译：基于最大抛物线正则性的Radau IIA方法的后验误差估计

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摘要

We consider the discretization of differential equations satisfying the maximal parabolic L-p-regularity property in Banach spaces by Radau IIA methods. We establish a posteriori error estimators via the maximal parabolic regularity of the differential equation. To complete the picture, we utilize the maximal parabolic regularity of the numerical methods to prove that the estimators are of optimal order.

机译：我们考虑了利用Radau IIA方法对满足Banach空间中最大抛物线L-p正则性质的微分方程进行离散化.我们通过微分方程的最大抛物线正则性建立了后验误差估计器.为了完成这幅图，我们利用数值方法的最大抛物线正则性来证明估计量是最优阶的。

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来源
《Numerische Mathematik》 |2022年第3期|691-717|共27页
作者
Akrivis Georgios; Makridakis Charalambos G.;
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作者单位

Univ Ioannina;

Univ Crete;

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原文格式 PDF
正文语种英语
中图分类数值分析;
关键词
A posteriori error estimates; Maximal parabolic regularity; Discrete maximal parabolic regularity; Radau IIA methods; FOURIER MULTIPLIER THEOREMS; CRANK-NICOLSON METHOD; DISCRETIZATIONS; EQUATIONS;

机译：后验误差估计;最大抛物线正则性;离散最大抛物线正则性;Radau IIA方法;傅里叶乘数THEOREMS;CRANK-NICOLSON方法;离散化;方程;

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2. Fully discrete a posteriori error estimates for parabolic integro-differential equations using the two-step backward differentiation formula [J] . Reddy G. Murali Mohan BIT numerical mathematics . 2022,第1期

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3. Functional A Posteriori Error Estimates for the Parabolic Obstacle Problem [J] . Apushkinskaya Darya, Repin Sergey Computational methods in applied mathematics . 2022,第2期

机译：Functional A Posteriori Error Estimates for the Parabolic Obstacle Problem
4. 过程工业中一种简易实用的过失误差识别与校正方法（A Simple and Practical Method for Detection of Gross Error in Process Industries） [C] . Chinese Control Conference vol.2; 20040810-13; Wuxi(CN) . 2004

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5. A 17th-order Radau IIA method for package RADAU. Applications in mechanical systems [O] . Martín-Vaquero J. 2010

机译：封装RADAU的17阶Radau IIA方法。机械系统中的应用

A posteriori error estimates for Radau IIA methods via maximal parabolic regularity

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