Academic Journal
Analysis of two thermoelastic problems with the Green–Lindsay model
| Τίτλος: | Analysis of two thermoelastic problems with the Green–Lindsay model |
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| Συγγραφείς: | Noelia Bazarra, José R. Fernández, Ramón Quintanilla |
| Συνεισφορές: | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
| Πηγή: | Investigo. Repositorio Institucional de la Universidade de Vigo Universidade de Vigo (UVigo) UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Στοιχεία εκδότη: | Springer Science and Business Media LLC, 2023. |
| Έτος έκδοσης: | 2023 |
| Θεματικοί όροι: | Finite elements, Classificació AMS::74 Mechanics of deformable solids::74F Coupling of solid mechanics with other effects, 1206 Análisis Numérico, 01 natural sciences, Classificació AMS::65 Numerical analysis::65M Partial differential equations, A priori error estimates, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències, initial value and time-dependent initial-boundary value problems, Discrete stability, Numerical simulations, Classificació AMS::65 Numerical analysis::65M Partial differential equations, initial value and time-dependent initial-boundary value problems, 0101 mathematics, Green–Lindsay, Dissipation mechanisms, Thermoelasticity, Termoelasticitat |
| Περιγραφή: | In this paper, we analyze, from the numerical point of view, two thermo-elastic problems involving the Green–Lindsay theory. The coupling term is different for each case, involving second order or first order spatial derivatives, respectively. The variational formulation leads to a linear coupled system which is written in terms of the velocity and temperature speed. An existence and uniqueness results and the exponential energy decay for the problem with the stronger coupling are recalled. The polynomial energy decay for the weaker coupling is then proved but using the theory of linear semigroups. Then, a fully discrete approximation is introduced using the finite element method and an implicit scheme. A discrete stability property and a main a priori error estimates result are shown, from which we can derive the linear convergence of the approximations. Finally, some numerical simulations are presented to demonstrate the accuracy of the algorithm, the discrete energy decay and the dependence on the relaxation parameter. |
| Τύπος εγγράφου: | Article |
| Περιγραφή αρχείου: | application/pdf |
| Γλώσσα: | English |
| ISSN: | 1807-0302 2238-3603 |
| DOI: | 10.1007/s40314-023-02335-5 |
| Σύνδεσμος πρόσβασης: | http://hdl.handle.net/11093/5281 https://link.springer.com/10.1007/s40314-023-02335-5 |
| Rights: | CC BY |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....b9b95395c0d22eb97577d34f6ae0012b |
| Βάση Δεδομένων: | OpenAIRE |
| ISSN: | 18070302 22383603 |
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| DOI: | 10.1007/s40314-023-02335-5 |