An a priori error analysis of a problem involving mixtures of continua with gradient enrichment

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.