Error estimates for approximate solutions of problems of the linear thermoelasticity theory
type: Item
instance of: scholarly article
title: Error estimates for approximate solutions of problems of the linear thermoelasticity theory
zbMATH Open document ID: 1162.74017
author: A. Muzalevskiy
author: Sergey Repin
published in: Russian Mathematics
publication date: 2007-05-22T00:00:00Z
review text: Majorants of the energetic norm of the deviation from the precise solution applicable to any functions from the energetic class are described in \textit{S. I. Repin}, J. Math. Sci., New York 99, No.1, 927--935 (2000) and Zap. Nauchn. Semin. POMI 243, 201--214 (1997; Zbl 0904.65064), Math. Comput. 69, No. 230, 481--500 (2000; Zbl 0949.65070), Transl., Ser. 2, Am. Math. Soc. 209, 143--171 (2003); translation from Tr. St-Peterbg. Mat. Obshch. 9, 148--179 (2001; Zbl 1039.65076)]. These majorants were obtained by the general methods of functional analysis and duality theory for the calculus of variations, therefore, they can be called a posteriori estimates of the functional type. They were investigated for problems of the linear elasticity theory in \textit{A. V. Muzalevsky} and \textit{S. I. Repin}, Russ. J. Numer. Anal. Math. Model. 18, No. 1, 65--85 (2003; Zbl 1027.74070)]. In this paper, this approach is used to obtain the functional type majorant for problems of the linear thermoelasticity theory and verify its efficiency by a number of test examples.
reviewed by: Elena Gavrilova
Mathematics Subject Classification ID: 74H15
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 74G65
zbMATH DE Number: 5155755
zbMATH Keywords: error estimates
zbMATH Keywords: approximate solutions
zbMATH Keywords: problems of the linear thermoelasticity theory
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5155755