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 - <p style="text-align: justify;">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.</p>