{"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}
引用次数: 0
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.
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.
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