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Volume 21, Issue 2
An a Priori Error Analysis of a Problem Involving Mixtures of Continua with Gradient Enrichment

Noelia Bazarra, José R. Fernández, Antonio Magaña, Marc Magaña & Ramόn Quintanilla

DOI: 10.4208/ijnam2024-1006

Int. J. Numer. Anal. Mod., 21 (2024), pp. 165-180.

Published online: 2024-04

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  • Abstract

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.

  • Keywords

Mixtures, strain gradient, finite elements, discrete energy decay, a priori error estimates, numerical simulations.

  • AMS Subject Headings

65M60, 65M15, 65M12, 74F20, 74A30

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-21-165, author = {Bazarra , NoeliaFernández , José R.Magaña , AntonioMagaña , Marc and Quintanilla , Ramόn}, title = {An a Priori Error Analysis of a Problem Involving Mixtures of Continua with Gradient Enrichment}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2024}, volume = {21}, number = {2}, pages = {165--180}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2024-1006}, url = {http://global-sci.org/intro/article_detail/ijnam/23022.html} }
TY - JOUR T1 - An a Priori Error Analysis of a Problem Involving Mixtures of Continua with Gradient Enrichment AU - Bazarra , Noelia AU - Fernández , José R. AU - Magaña , Antonio AU - Magaña , Marc AU - Quintanilla , Ramόn JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 165 EP - 180 PY - 2024 DA - 2024/04 SN - 21 DO - http://doi.org/10.4208/ijnam2024-1006 UR - https://global-sci.org/intro/article_detail/ijnam/23022.html KW - Mixtures, strain gradient, finite elements, discrete energy decay, a priori error estimates, numerical simulations. AB -

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.

Bazarra , NoeliaFernández , José R.Magaña , AntonioMagaña , Marc and Quintanilla , Ramόn. (2024). An a Priori Error Analysis of a Problem Involving Mixtures of Continua with Gradient Enrichment. International Journal of Numerical Analysis and Modeling. 21 (2). 165-180. doi:10.4208/ijnam2024-1006
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