Fully discrete approximations and an a priori error analysis of a two-temperature thermo-elastic model with microtemperatures. (English) Zbl 07875991
Summary: In this paper, we consider, from a numerical point of view, a two-temperature poro-thermoelastic problem. The model is written as a coupled linear system of hyperbolic and elliptic partial differential equations. An existence result is proved and energy decay properties are recalled. Then we introduce a fully discrete approximation by using the finite element method and the implicit Euler scheme. Some a priori error estimates are obtained, from which the linear convergence of the approximation is deduced under an appropriate additional regularity. Finally, some numerical simulations are performed to demonstrate the accuracy of the approximation, the decay of the discrete energy and the behaviour of the solution depending on a constitutive parameter.
MSC:
| 74F05 | Thermal effects in solid mechanics |
| 74F15 | Electromagnetic effects in solid mechanics |
| 74H20 | Existence of solutions of dynamical problems in solid mechanics |
| 74H40 | Long-time behavior of solutions for dynamical problems in solid mechanics |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74S20 | Finite difference methods applied to problems in solid mechanics |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
Keywords:
hyperbolic-elliptic linear system; solution existence; energy decay; finite element method; implicit Euler scheme; error estimateReferences:
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