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Int. J. Numer. Anal. Mod., 21 (2024), pp. 165-180.
Published online: 2024-04
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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} }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.