用一组数值解估计点向逼近误差

IF 0.4 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications Pub Date : 2022-12-08 DOI:10.1134/s1995423922040012

A. K. Alekseev, A. E. Bondarev

{"title":"用一组数值解估计点向逼近误差","authors":"A. K. Alekseev, A. E. Bondarev","doi":"10.1134/s1995423922040012","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This paper deals with estimation of local (pointwise) approximation error on an ensemble of numerical solutions obtained by using independent algorithms. A variational inverse problem is posed for approximation error estimation. This problem is ill-posed due to translation-invariance of the governing equations. Zero order Tikhonov regularization is applied to obtain stable solutions. Numerical tests for two-dimensional equations describing inviscid compressible flow are performed to verify the efficiency of the algorithm. The approximation error estimates obtained by using the inverse problem are in satisfactory agreement with those obtained by Richardson extrapolation, but with significantly less computational costs.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"32 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Estimation of Pointwise Approximation Error Using a Set of Numerical Solutions\",\"authors\":\"A. K. Alekseev, A. E. Bondarev\",\"doi\":\"10.1134/s1995423922040012\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>This paper deals with estimation of local (pointwise) approximation error on an ensemble of numerical solutions obtained by using independent algorithms. A variational inverse problem is posed for approximation error estimation. This problem is ill-posed due to translation-invariance of the governing equations. Zero order Tikhonov regularization is applied to obtain stable solutions. Numerical tests for two-dimensional equations describing inviscid compressible flow are performed to verify the efficiency of the algorithm. The approximation error estimates obtained by using the inverse problem are in satisfactory agreement with those obtained by Richardson extrapolation, but with significantly less computational costs.</p>\",\"PeriodicalId\":43697,\"journal\":{\"name\":\"Numerical Analysis and Applications\",\"volume\":\"32 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-12-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Numerical Analysis and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1134/s1995423922040012\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Analysis and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995423922040012","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

摘要本文研究了用独立算法求得的数值解集合的局部(点向)逼近误差的估计。提出了近似误差估计的变分反问题。由于控制方程的平移不变性，这个问题是不适定的。采用零阶Tikhonov正则化得到稳定解。通过二维无粘可压缩流动方程的数值试验，验证了该算法的有效性。利用反问题得到的近似误差估计与Richardson外推法得到的近似误差估计有较好的一致性，但计算成本明显减少。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Estimation of Pointwise Approximation Error Using a Set of Numerical Solutions

查看原文本刊更多论文

Estimation of Pointwise Approximation Error Using a Set of Numerical Solutions

Abstract

This paper deals with estimation of local (pointwise) approximation error on an ensemble of numerical solutions obtained by using independent algorithms. A variational inverse problem is posed for approximation error estimation. This problem is ill-posed due to translation-invariance of the governing equations. Zero order Tikhonov regularization is applied to obtain stable solutions. Numerical tests for two-dimensional equations describing inviscid compressible flow are performed to verify the efficiency of the algorithm. The approximation error estimates obtained by using the inverse problem are in satisfactory agreement with those obtained by Richardson extrapolation, but with significantly less computational costs.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Numerical Analysis and Applications MATHEMATICS, APPLIED-

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Numerical Analysis and Applications is the translation of Russian periodical Sibirskii Zhurnal Vychislitel’noi Matematiki (Siberian Journal of Numerical Mathematics) published by the Siberian Branch of the Russian Academy of Sciences Publishing House since 1998. The aim of this journal is to demonstrate, in concentrated form, to the Russian and International Mathematical Community the latest and most important investigations of Siberian numerical mathematicians in various scientific and engineering fields. The journal deals with the following topics: Theory and practice of computational methods, mathematical physics, and other applied fields; Mathematical models of elasticity theory, hydrodynamics, gas dynamics, and geophysics; Parallelizing of algorithms; Models and methods of bioinformatics.