Numerical analysis of a problem of elasticity with several dissipation mechanisms
In this work, we numerically study a problem including several dissipative mechanisms. A particular case involving the symmetry of the coupling matrix and three mechanisms is considered, leading to the exponential decay of the corresponding solutions. Then, a fully discrete approximation of the gene...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/381176 |
| Acceso en línea: | https://hdl.handle.net/2117/381176 https://dx.doi.org/10.1007/s11012-022-01628-z |
| Access Level: | acceso abierto |
| Palabra clave: | Thermoelasticity Dissipation mechanisms Finite elements A priori error estimates Numerical simulations Discrete energy decay Termoelasticitat Classificació AMS::65 Numerical analysis::65M Partial differential equations, initial value and time-dependent initial-boundary value problems Classificació AMS::74 Mechanics of deformable solids::74F Coupling of solid mechanics with other effects Classificació AMS::74 Mechanics of deformable solids::74K Thin bodies, structures Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències |
| Sumario: | In this work, we numerically study a problem including several dissipative mechanisms. A particular case involving the symmetry of the coupling matrix and three mechanisms is considered, leading to the exponential decay of the corresponding solutions. Then, a fully discrete approximation of the general case in two dimensions is introduced by using the finite element method and the implicit Euler scheme. A priori error estimates are obtained and the linear convergence is derived under some appropriate regularity conditions on the continuous solution. Finally, some numerical simulations are performed to illustrate the numerical convergence and the behavior of the discrete energy depending on the number of dissipative mechanisms |
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