Numerical approximation of some poro-elastic problems with MGT-type dissipation mechanisms

Abstract

In this work, we numerically analyze a porous elastic problem including several dissipation mechanisms of MGT type. The resulting variational problem is written in terms of the acceleration and the porosity speed. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced by using the classical 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 approximation is derived. Finally, some numerical simulations are presented to show the accuracy of the approximation, the discrete energy decay and the behavior of the solution.