Abstract
In this work, we study a thermoelastic Bresse system from both mathematical and numerical points of view. The dual-phase-lag heat conduction theory is used to model the heat transfer. An existence and uniqueness result is obtained by using the theory of linear semigroups. Then, fully discrete approximations are introduced by using the finite element method and the implicit Euler scheme. A priori error estimates are shown, from which the linear convergence is derived under suitable regularity conditions. Finally, some numerical simulations are presented to demonstrate the accuracy of the approximation and the behavior of the solution with respect to a constitutive parameter.
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Acknowledgements
The authors thank the anonymous referee for his (her) criticism that allowed us to improve the manuscript. The work of J.R. Fernández has been partially supported by Ministerio de Ciencia, Innovación y Universidades under the research project PGC2018-096696-B-I00 (FEDER, UE).
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Bazarra, N., Bochicchio, I., Fernández, J.R. et al. Thermoelastic Bresse system with dual-phase-lag model. Z. Angew. Math. Phys. 72, 102 (2021). https://doi.org/10.1007/s00033-021-01536-4
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DOI: https://doi.org/10.1007/s00033-021-01536-4