A high-order discontinuous Galerkin method for the poro-elasto-acoustic problem on polygonal and polyhedral grids

The aim of this work is to introduce and analyze a finite element discontinuous Galerkin method on polygonal meshes for the numerical discretization of acoustic waves propagation through poroelastic materials. Wave propagation is modeled by the acoustics equations in the acoustic domain and the low-frequency Biot's equations in the poroelastic one. The coupling is introduced by considering (physically consistent) interface conditions, imposed on the interface between the domains, modeling both open and sealed pores. Existence and uniqueness is proven for the strong formulation based on employing the semigroup theory. For the space discretization we introduce and analyze a high-order discontinuous Galerkin method on polygonal and polyhedral meshes, which is then coupled with Newmark-$\beta$ time integration schemes. A stability analysis both for the continuous problem and the semi-discrete one is presented and error estimates for the energy norm are derived for the semidiscrete problem. A wide set of numerical results obtained on test cases with manufactured solutions are presented in order to validate the error analysis. Examples of physical interest are also presented to test the capability of the proposed methods in practical cases.