Analysis of finite element methods for dynamic poroelasticity: Low frequency waves

In this paper we consider a finite element discretization of low-frequency dynamic poroelasticity models and carry out the a priori error analysis. In contrast to the widely used quasi-static poroelasticity models, the dynamic models are hyperbolic partial differential equations with acceleration terms of solid and fluid phases. We reformulate the problem to a symmetric hyperbolic system and discretize it with two mixed finite element methods. The error analysis semidiscrete solutions are discussed in detail and numerical results of the backward Euler fully discrete scheme are presented. (C) 2022 Elsevier B.V. All rights reserved.