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In this work we review discontinuous Galerkin finite element methods onpolytopal grids (PolydG) for the numerical simulation of multiphysics wavepropagation phenomena in heterogeneous media. In particular, we address wavephenomena in elastic, poro-elastic, and poro-elasto-acoustic materials. Wavepropagation is modeled by using either the elastodynamics equation in theelastic domain, the acoustics equations in the acoustic domain and thelow-frequency Biot's equations in the poro-elastic one. The coupling betweendifferent models is realized by means of (physically consistent) transmissionconditions, weakly imposed at the interface between the subdomains. For allmodels configuration, we introduce and analyse the PolydG semi-discreteformulation, which is then coupled with suitable time marching schemes. For thesemi-discrete problem, we present the stability analysis and derive a-priorierror estimates in a suitable energy norm. A wide set of verification testswith manufactured solutions are presented in order to validate the erroranalysis. Examples of physical interest are also shown to demonstrate thecapability of the proposed methods.

On mathematical and numerical modelling of multiphysics wave propagation with polytopal Discontinuous Galerkin methods