descriptionPublicationkeyboard_double_arrow_right Article 26 Dec 2022 English Publisher:Springer Science and Business Media LLCJournal:Meccanica, volume 58, pages 179-191 (issn: 0025-6455, eissn: 1572-9648,

Authors: Bazarra, Noelia; Fernández, Jose R.; Quintanilla de Latorre, Ramón;

doi: 10.1007/s11012-022-01628-z

handle: 11093/4596 , 2117/381176

Numerical analysis of a problem of elasticity with several dissipation mechanisms

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Abstract

AbstractIn 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.

Related Organizations

Universitat Politècnica de Catalunya
Spain
Universitat Polite`cnica de Catalunya
Spain
Universidade de Vigo
Spain

Keywords

Discrete energy decay, Classificació AMS::74 Mechanics of deformable solids::74K Thin bodies, Finite elements, Classificació AMS::74 Mechanics of deformable solids::74F Coupling of solid mechanics with other effects, 1202 Análisis y Análisis Funcional, 1206 Análisis Numérico, structures, 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, Numerical simulations, Classificació AMS::74 Mechanics of deformable solids::74K Thin bodies, structures, Classificació AMS::65 Numerical analysis::65M Partial differential equations, initial value and time-dependent initial-boundary value problems, Dissipation mechanisms, Thermoelasticity, Termoelasticitat

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