2026-04-14T03:20:59Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/4439952026-01-30T01:42:53Zcom_2072_1033col_2072_452950

An a priori error analysis of a thermoelastic problem with history dependence on the mechanical and thermal components Bazarra, Noelia Fernández García, José Ramón Quintanilla de Latorre, Ramón Universitat Politècnica de Catalunya. Departament de Matemàtiques Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències Thermoelasticity of MGT type Finite history Finite elements Stability Error estimates Numerical simulations Here, we provide an a priori error analysis of a thermoelastic problem, with the Moore–Gibson–Thompson (MGT) equation, where the history dependence is assumed on both the mechanical and thermal parts. An existence and uniqueness result, and the exponential stability, are recalled. Then, a fully discrete approximation is introduced by using the finite element method and the implicit Euler scheme, to approximate the spatial variable and the time derivatives, respectively. A discrete stability property is proved and a main a priori error estimates result is obtained. The linear convergence of the approximations is deduced under suitable regularity conditions. Finally, we perform some one- and two-dimensional simulations to show the accuracy of the algorithm, the exponential decay of the discrete energy and the behavior of the solution. This paper is part of the project “Qualitative and numerical analyses of some thermomechanical problems (ACUANUTER)” (Ref. PID2024-156827NB-I00), which is currently under evaluation by the Spanish Ministry of Science, Innovation and Universities Peer Reviewed Postprint (published version) 2026-02 Article Bazarra, N.; Fernández, J.; Quintanilla, R. An a priori error analysis of a thermoelastic problem with history dependence on the mechanical and thermal components. «Journal of computational and applied mathematics», Febrer 2026, vol. 473, núm. article 116883. 0377-0427 https://hdl.handle.net/2117/443995 10.1016/j.cam.2025.116883 eng https://www.sciencedirect.com/science/article/pii/S0377042725003978 http://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access Attribution-NonCommercial-NoDerivatives 4.0 International 12 p. application/pdf