An a priori error analysis of a porous strain gradient model

Abstract

In this work, we consider, from the numerical point of view, a boundary-initial value problem for non-simple porous elastic materials. The mechanical problem is written as a coupled hyperbolic linear system in terms of the displacement and porosity fields. The resulting variational formulation is used to approximate the solution by the finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are proved, from which the linear convergence of the numerical scheme is deduced under adequate regularity conditions. Finally, some numerical simulations are presented to show the accuracy of the finite element scheme studied previously, the evolution of the discrete energy and the behavior of the solution.

Decay of waves in strain gradient porous elasticity with Moore–Gibson–Thompson dissipation

“…However, whether the decay can be controlled by a polynomial is still an open question. Let us end this study by comparing the decay of the waves when MGT-dissipation mechanisms are taken into account with their decay when the classical KV dissipation is considered. In a recent study [35], the authors prove that under KV viscoelasticity, the waves dampen uniformly, that is, the elements of the spectrum are quite far away from the imaginary axis. Instead, if MGT-dissipation is considered, the elements of the spectrum approach the imaginary axis.…”