Discontinuous Galerkin discretization of coupled poroelasticity-elasticity problems
This work provides a rigorous numerical framework for simulating coupled poroelastic-elastic wave propagation, which is important for geophysical applications like seismic modeling.
The authors developed and analyzed a space-time discontinuous Galerkin method for wave propagation in coupled poroelastic-elastic media, proving stability and error estimates, and verifying them with numerical tests.
This work is concerned with the analysis of a space-time finite element discontinuous Galerkin method on polytopal meshes (XT-PolydG) for the numerical discretization of wave propagation in coupled poroelastic-elastic media. The mathematical model consists of the low-frequency Biot's equations in the poroelastic medium and the elastodynamics equation for the elastic one. To realize the coupling, suitable transmission conditions on the interface between the two domains are (weakly) embedded in the formulation. The proposed PolydG discretization in space is then coupled with a dG time integration scheme, resulting in a full space-time dG discretization. We present the stability analysis for both the continuous and the semidiscrete formulations, and we derive error estimates for the semidiscrete formulation in a suitable energy norm. The method is applied to a wide set of numerical test cases to verify the theoretical bounds. Examples of physical interest are also presented to investigate the capability of the proposed method in relevant geophysical scenarios.