Volume 17, Issue 2
On the Linear Thermoelasticity with Two Porosities: Numerical Aspects

Noelia Bazarra, José R. Fernández, Mari Carme Leseduarte, Antonio Magaña & Ramón Quintanilla

Int. J. Numer. Anal. Mod., 17 (2020), pp. 172-194.

Published online: 2020-02

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  • Abstract

In this work we analyze, from the numerical point of view, a dynamic problem involving a thermoelastic rod. Two porosities are considered: the first one is the macro-porosity, connected with the pores of the material, and the other one is the micro-porosity, linked with the fissures of the skeleton. The mechanical problem is written as a set of hyperbolic and parabolic partial differential equations. An existence and uniqueness result and an energy decay property are stated. Then, a fully discrete approximation is introduced using the finite element method and the backward Euler scheme. A discrete stability property and a priori error estimates are proved, from which the linear convergence of the algorithm is derived under suitable additional regularity conditions. Finally, some numerical simulations are presented to show the behaviour of the approximation.

  • Keywords

Thermoelasticity with two porosities, finite elements, a priori error estimates, numerical simulations.

  • AMS Subject Headings

65M60, 65M15, 65M12, 74K10, 74F05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

noabaza@hotmail.com (Noelia Bazarra)

jose.fernandez@uvigo.es (José R. Fernández)

Mari.Carme.Leseduarte@upc.edu (Mari Carme Leseduarte)

antonio.magana@upc.edu (Antonio Magaña)

Ramon.Quintanilla@upc.edu (Ramón Quintanilla)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-17-172, author = {Bazarra , Noelia and Fernández , José R. and Leseduarte , Mari Carme and Magaña , Antonio and Quintanilla , Ramón}, title = {On the Linear Thermoelasticity with Two Porosities: Numerical Aspects}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {2}, pages = {172--194}, abstract = {

In this work we analyze, from the numerical point of view, a dynamic problem involving a thermoelastic rod. Two porosities are considered: the first one is the macro-porosity, connected with the pores of the material, and the other one is the micro-porosity, linked with the fissures of the skeleton. The mechanical problem is written as a set of hyperbolic and parabolic partial differential equations. An existence and uniqueness result and an energy decay property are stated. Then, a fully discrete approximation is introduced using the finite element method and the backward Euler scheme. A discrete stability property and a priori error estimates are proved, from which the linear convergence of the algorithm is derived under suitable additional regularity conditions. Finally, some numerical simulations are presented to show the behaviour of the approximation.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/13646.html} }
TY - JOUR T1 - On the Linear Thermoelasticity with Two Porosities: Numerical Aspects AU - Bazarra , Noelia AU - Fernández , José R. AU - Leseduarte , Mari Carme AU - Magaña , Antonio AU - Quintanilla , Ramón JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 172 EP - 194 PY - 2020 DA - 2020/02 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/13646.html KW - Thermoelasticity with two porosities, finite elements, a priori error estimates, numerical simulations. AB -

In this work we analyze, from the numerical point of view, a dynamic problem involving a thermoelastic rod. Two porosities are considered: the first one is the macro-porosity, connected with the pores of the material, and the other one is the micro-porosity, linked with the fissures of the skeleton. The mechanical problem is written as a set of hyperbolic and parabolic partial differential equations. An existence and uniqueness result and an energy decay property are stated. Then, a fully discrete approximation is introduced using the finite element method and the backward Euler scheme. A discrete stability property and a priori error estimates are proved, from which the linear convergence of the algorithm is derived under suitable additional regularity conditions. Finally, some numerical simulations are presented to show the behaviour of the approximation.

Noelia Bazarra, José R. Fernández, Mari Carme Leseduarte, Antonio Magaña & Ramón Quintanilla. (2020). On the Linear Thermoelasticity with Two Porosities: Numerical Aspects. International Journal of Numerical Analysis and Modeling. 17 (2). 172-194. doi:
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