A LOCAL DISCONTINUOUS GALERKIN APPROXIMATION FOR THE p-NAVIER-STOKES SYSTEM, PART I: CONVERGENCE ANALYSIS.

In the present paper, we propose a local discontinuous Galerkin approximation for fully nonhomogeneous systems of p-Navier--Stokes type. On the basis of the primal formulation, we prove well-posedness, stability (a priori estimates), and weak convergence of the method. To this end, we propose a new discontinuous Galerkin discretization of the convective term and develop an abstract nonconforming theory of pseudomonotonicity, which is applied to our problem. We also use our approach to treat the p-Stokes problem. [ABSTRACT FROM AUTHOR]