Stability and Numerical Analysis of Micropolar Viscoelastic Systems

In this work, we consider two dynamic systems arising in micropolar viscoelasticity. In this sense, the material structure is assumed to have macroscopic and microscopic levels. First, an existence and uniqueness result is proved by using the theory of linear semigroups and, secondly, the decay of t...

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Published in:	Journal of elasticity Vol. 157; no. 4; p. 83
Main Authors:	Bazarra, Noelia, Fernández, José R., Fernández Sare, Hugo D., Quintanilla, Ramón
Format:	Journal Article
Language:	English
Published:	Dordrecht Springer Netherlands 01.11.2025 Springer Nature B.V
Subjects:	Approximation Biomechanics Boundary conditions Classical and Continuum Physics Classical Mechanics Convergence Decay Dynamical systems Engineering Equilibrium Error analysis Finite element analysis Finite element method Materials Science Mathematical analysis Mathematical Applications in the Physical Sciences Mathematical problems Numerical analysis Operators (mathematics) Partial differential equations Polynomials Stability Theoretical and Applied Mechanics Viscoelasticity Viscoelasticity 65M15 Micropolar Finite elements Stability Numerical analysis 35B35 74F99 65M60 35B40 Existence and uniqueness
ISSN:	0374-3535, 1573-2681
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Abstract	In this work, we consider two dynamic systems arising in micropolar viscoelasticity. In this sense, the material structure is assumed to have macroscopic and microscopic levels. First, an existence and uniqueness result is proved by using the theory of linear semigroups and, secondly, the decay of the solutions to the equilibrium state is shown. Then, the polynomial energy decay is obtained applying a characterization of the system operator. In a second part, we consider the numerical approximation of a variational version of the above problem. This is done by using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A discrete stability property is proved and an a priori error analysis is provided. The linear convergence of the approximations is deduced under some additional regularity conditions on the continuous solution. Finally, some numerical simulations are shown to demonstrate numerical convergence and the behavior of the discrete energy.
AbstractList	In this work, we consider two dynamic systems arising in micropolar viscoelasticity. In this sense, the material structure is assumed to have macroscopic and microscopic levels. First, an existence and uniqueness result is proved by using the theory of linear semigroups and, secondly, the decay of the solutions to the equilibrium state is shown. Then, the polynomial energy decay is obtained applying a characterization of the system operator. In a second part, we consider the numerical approximation of a variational version of the above problem. This is done by using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A discrete stability property is proved and an a priori error analysis is provided. The linear convergence of the approximations is deduced under some additional regularity conditions on the continuous solution. Finally, some numerical simulations are shown to demonstrate numerical convergence and the behavior of the discrete energy.
ArticleNumber	83
Author	Fernández Sare, Hugo D. Fernández, José R. Bazarra, Noelia Quintanilla, Ramón
Author_xml	– sequence: 1 givenname: Noelia surname: Bazarra fullname: Bazarra, Noelia organization: Departamento de Matemática Aplicada I, Universidade de Vigo – sequence: 2 givenname: José R. surname: Fernández fullname: Fernández, José R. email: jose.fernandez@uvigo.es organization: Departamento de Matemática Aplicada I, Universidade de Vigo – sequence: 3 givenname: Hugo D. surname: Fernández Sare fullname: Fernández Sare, Hugo D. organization: Departamento de Matemática, Universidade Federal de Juiz de Fora – sequence: 4 givenname: Ramón surname: Quintanilla fullname: Quintanilla, Ramón organization: Department of Mathematics, UPC
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Snippet	In this work, we consider two dynamic systems arising in micropolar viscoelasticity. In this sense, the material structure is assumed to have macroscopic and...
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SubjectTerms	Approximation Biomechanics Boundary conditions Classical and Continuum Physics Classical Mechanics Convergence Decay Dynamical systems Engineering Equilibrium Error analysis Finite element analysis Finite element method Materials Science Mathematical analysis Mathematical Applications in the Physical Sciences Mathematical problems Numerical analysis Operators (mathematics) Partial differential equations Polynomials Stability Theoretical and Applied Mechanics Viscoelasticity
Title	Stability and Numerical Analysis of Micropolar Viscoelastic Systems
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