An a priori error analysis of a problem involving mixtures of continua with gradient enrichment
In this work, we study a strain gradient problem involving mixtures. The variational formulation is written as a first-order in time coupled system of parabolic variational equations. An existence and uniqueness result is recalled. Then, we introduce a fully discrete approximation by using the finit...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| 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:2117/408116 |
| Acceso en línea: | https://hdl.handle.net/2117/408116 https://dx.doi.org/10.4208/ijnam2024-1006 |
| Access Level: | acceso abierto |
| Palabra clave: | Thermoelasticity Finite element method Mixtures Strain gradient Finite elements Discrete energy decay A priori error estimates Numerical simulations Termoelasticitat Elements finits, Mètode dels 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::74A Generalities, axiomatics, foundations of continuum mechanics of solids Classificació AMS::74 Mechanics of deformable solids::74F Coupling of solid mechanics with other effects Classificació AMS::74 Mechanics of deformable solids::74H Dynamical problems Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències |
| Sumario: | In this work, we study a strain gradient problem involving mixtures. The variational formulation is written as a first-order in time coupled system of parabolic variational equations. An existence and uniqueness result is recalled. Then, we introduce a fully discrete approximation by using the finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are proved. Finally, some one- and two-dimensional numerical simulations are performed. |
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