{"title":"A New A Posteriori Error Estimates for Optimal Control Problems Governed by Parabolic Integro-Differential Equations","authors":"H. Chen, T. Hou","doi":"10.1134/s1995423924010075","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we provide a new a posteriori error analysis for linear finite element approximation of a parabolic integro-differential optimal control problem. The state and co-state are approximated by piecewise linear functions, while the control variable is discretized by variational discretization method. We first define the elliptic reconstructions of numerical solutions and then discuss a posteriori error estimates for all variables.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"22 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-03-13","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/s1995423924010075","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
In this paper, we provide a new a posteriori error analysis for linear finite element approximation of a parabolic integro-differential optimal control problem. The state and co-state are approximated by piecewise linear functions, while the control variable is discretized by variational discretization method. We first define the elliptic reconstructions of numerical solutions and then discuss a posteriori error estimates for all variables.
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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