Mixed virtual element methods for the poro-elastodynamics model on polygonal grids

This work introduces and analyzes the mixed virtual element method on polygonal meshes for the numerical discretization of poro-elastodynamics models. For spatial discretization, we employ the mixed virtual element method on polygonal meshes, coupled with Newmark-β integration schemes for time discretization. We present a stability analysis for both the continuous and semi-discrete problems and derive error estimates for the energy norm in the semi-discrete case. Numerical experiments are conducted to verify the theoretical analysis, and the results on Voronoi meshes demonstrate that the algorithm effectively handles various dynamic viscosities.