Optimal order FEM for dynamic poroelasticity: Error analysis for equal order elements

The numerical approximation of dynamic poroelasticity, modeling flow in deformable porous media, by a family of continuous space-time finite element methods is investigated. Equal order approximation in space without any further stabilization is used for the displacement and pore pressure variable. Optimal order $L^{\mathrm{\infty }}(L^2)$ error estimates are proved and numerically confirmed.