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...

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Detalles Bibliográficos
Autores: Bazarra, Noelia, Fernández García, José Ramón|||0000-0002-8533-1858, Magaña Nieto, Antonio|||0000-0003-0879-0759, Quintanilla de Latorre, Ramón|||0000-0001-7059-7058, Magaña Centelles, Marc
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
Descripción
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.