Implementation of HDG method for 2D anisotropic poroelastic first-order harmonic equations

In this report, we develop a Hybridizable Discontinuous Galerkin (HDG) methodapplied to solving the two-dimensional anisotropic poroelastic equations written as a first-ordersystem in the frequency domain. We motivate the choice of the HDG method by the complexity ofthe considered equations and the high number of unknowns. The HDG method possesses indeedall the advantages of Discontinuous Galerkin method (hp-adaptivity, accuracy, ability to modelrugged domain,...) without its main drawback, the dramatic increase of the number of degrees offreedom. We illustrate the accuracy of the proposed solution methodology thanks to numericalexperiments and comparisons with analytical solutions that were developed in another work. Wealso offer numerical implementations on realistic geophysical media.