Error analysis of primal discontinuous Galerkin methods for a mixed formulation of the Biot equations

A novel mixed formulation of the Biot equations of poroelasticity is proposed motivated by an application in the biomechanics of edema formation in intestinal tissue. The mixed formulation is discretized by two variants of the primal discontinuous Galerkin method in conjunction with a backward Euler timestepping. An a-priori error analysis for the symmetric and non-symmetric establishes rates of convergence in the L2 and energy norms. Convergence of the scheme is further investigated numerically.