Hybridizable discontinuous Galerkin method for dynamic poroelasticity: an <i>hp</i> -error analysis

Abstract This study introduces a hybridizable discontinuous Galerkin (HDG) method for simulating low-frequency wave propagation in poroelastic media. We present a novel four-field variational formulation and establish its well-posedness and energy stability. Our hp -convergence analysis of the HDG method for spatial discretization is complemented by a Crank–Nicolson scheme for temporal discretization. Numerical experiments validate the theoretical convergence rates and demonstrate the effectiveness of the method in accurately capturing poroelastic dynamics.