On the mixtures of MGT viscoelastic solids
In this paper, we study, from both analytical and numerical points of view, a problem involving a mixture of two viscoelastic solids. An existence and uniqueness result is proved using the theory of linear semigroups. Exponential decay is shown for the one-dimensional case. Then, fully discrete appr...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-09-01
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| Series: | Electronic Research Archive |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2022219?viewType=HTML |
| _version_ | 1811220078303117312 |
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| author | Noelia Bazarra José R. Fernández Ramón Quintanilla |
| author_facet | Noelia Bazarra José R. Fernández Ramón Quintanilla |
| author_sort | Noelia Bazarra |
| collection | DOAJ |
| description | In this paper, we study, from both analytical and numerical points of view, a problem involving a mixture of two viscoelastic solids. An existence and uniqueness result is proved using the theory of linear semigroups. Exponential decay is shown for the one-dimensional case. Then, fully discrete approximations are introduced using the finite element method and the implicit Euler scheme. Some a priori error estimates are obtained and the linear convergence is derived under suitable regularity conditions. Finally, one- and two-dimensional numerical simulations are presented to demonstrate the convergence, the discrete energy decay and the behavior of the solution. |
| first_indexed | 2024-04-12T07:35:45Z |
| format | Article |
| id | doaj.art-691ce35e73fd477fb42d3db13f323c42 |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-04-12T07:35:45Z |
| publishDate | 2022-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-691ce35e73fd477fb42d3db13f323c422022-12-22T03:41:57ZengAIMS PressElectronic Research Archive2688-15942022-09-0130124318434010.3934/era.2022219On the mixtures of MGT viscoelastic solidsNoelia Bazarra0José R. Fernández 1Ramón Quintanilla21. Departamento de Matemática Aplicada I, Universidade de Vigo, Escola de Enxeñería de Telecomunicación, Campus As Lagoas Marcosende s/n, Vigo 36310, Spain1. Departamento de Matemática Aplicada I, Universidade de Vigo, Escola de Enxeñería de Telecomunicación, Campus As Lagoas Marcosende s/n, Vigo 36310, Spain2. Departamento de Matemáticas, E.S.E.I.A.A.T.-U.P.C., Colom 11, Terrassa 08222, Barcelona, SpainIn this paper, we study, from both analytical and numerical points of view, a problem involving a mixture of two viscoelastic solids. An existence and uniqueness result is proved using the theory of linear semigroups. Exponential decay is shown for the one-dimensional case. Then, fully discrete approximations are introduced using the finite element method and the implicit Euler scheme. Some a priori error estimates are obtained and the linear convergence is derived under suitable regularity conditions. Finally, one- and two-dimensional numerical simulations are presented to demonstrate the convergence, the discrete energy decay and the behavior of the solution.https://www.aimspress.com/article/doi/10.3934/era.2022219?viewType=HTMLmixturesviscoelasticitylinear semigroupsexistence and uniquenessenergy decayfinite elements |
| spellingShingle | Noelia Bazarra José R. Fernández Ramón Quintanilla On the mixtures of MGT viscoelastic solids Electronic Research Archive mixtures viscoelasticity linear semigroups existence and uniqueness energy decay finite elements |
| title | On the mixtures of MGT viscoelastic solids |
| title_full | On the mixtures of MGT viscoelastic solids |
| title_fullStr | On the mixtures of MGT viscoelastic solids |
| title_full_unstemmed | On the mixtures of MGT viscoelastic solids |
| title_short | On the mixtures of MGT viscoelastic solids |
| title_sort | on the mixtures of mgt viscoelastic solids |
| topic | mixtures viscoelasticity linear semigroups existence and uniqueness energy decay finite elements |
| url | https://www.aimspress.com/article/doi/10.3934/era.2022219?viewType=HTML |
| work_keys_str_mv | AT noeliabazarra onthemixturesofmgtviscoelasticsolids AT joserfernandez onthemixturesofmgtviscoelasticsolids AT ramonquintanilla onthemixturesofmgtviscoelasticsolids |