Year: 2024
Author: Noelia Bazarra, José R. Fernández, Antonio Magaña, Marc Magaña, Ramόn Quintanilla
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2024-1006
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 2 : pp. 165–180
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Mixtures strain gradient finite elements discrete energy decay a priori error estimates numerical simulations.