{"title":"On an Optimal AFEM for Elastoplasticity","authors":"Miriam Schönauer, Andreas Schröder","doi":"10.1515/cmam-2024-0052","DOIUrl":null,"url":null,"abstract":"In this paper, optimal convergence for an adaptive finite element algorithm for elastoplasticity is considered. To this end, the proposed adaptive algorithm is established within the abstract framework of the axioms of adaptivity [C. Carstensen, M. Feischl, M. Page and D. Praetorius, Axioms of adaptivity, Comput. Math. Appl. 67 2014, 6, 1195–1253], which provides a specific proceeding to prove the optimal convergence of the scheme. The proceeding is based on verifying four axioms, which ensure the optimal convergence. The verification is done by using results from [C. Carstensen, A. Schröder and S. Wiedemann, An optimal adaptive finite element method for elastoplasticity, Numer. Math. 132 2016, 1, 131–154], which presents an alternative approach to optimality without explicitly relying on the axioms","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"10 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/cmam-2024-0052","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, optimal convergence for an adaptive finite element algorithm for elastoplasticity is considered. To this end, the proposed adaptive algorithm is established within the abstract framework of the axioms of adaptivity [C. Carstensen, M. Feischl, M. Page and D. Praetorius, Axioms of adaptivity, Comput. Math. Appl. 67 2014, 6, 1195–1253], which provides a specific proceeding to prove the optimal convergence of the scheme. The proceeding is based on verifying four axioms, which ensure the optimal convergence. The verification is done by using results from [C. Carstensen, A. Schröder and S. Wiedemann, An optimal adaptive finite element method for elastoplasticity, Numer. Math. 132 2016, 1, 131–154], which presents an alternative approach to optimality without explicitly relying on the axioms
本文考虑了弹塑性自适应有限元算法的最佳收敛性。为此，本文在自适应公理的抽象框架内建立了所提出的自适应算法[C. Carstensen, M. Feischl, M. Page and D. Praetorius, 《弹性力学》]。Carstensen, M. Feischl, M. Page and D. Praetorius, Axioms of adaptivity, Comput.Math.67 2014, 6, 1195-1253]，它提供了证明方案最优收敛性的具体程序。该程序基于对四个公理的验证，这四个公理确保了最优收敛性。验证是利用 [C. Carstensen, A. Sch.Carstensen, A. Schröder and S. Wiedemann, An optimal adaptive finite element method for elastoplasticity, Numer.Math.132 2016, 1, 131-154] 中的结果，它提出了另一种不明确依赖公理的最优方法
期刊介绍：
The highly selective international mathematical journal Computational Methods in Applied Mathematics (CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs.
CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics.
The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.
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