Error estimates for approximate solutions of problems of the linear thermoelasticity theory
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.
problems of the linear thermoelasticity theory
scientific article; zbMATH DE number 5155755