An embedded–hybridized discontinuous Galerkin finite element method for the Stokes equations

Abstract

We present and analyze a new embedded–hybridized discontinuous Galerkin finite element method for the Stokes problem. The method has the attractive properties of full hybridized methods, namely an H(div)-conforming velocity field, pointwise satisfaction of the continuity equation and a priori error estimates for the velocity that are independent of the pressure. The embedded–hybridized formulation has advantages over a full hybridized formulation in that it has fewer global degrees-of-freedom for a given mesh and the algebraic structure of the resulting linear system is better suited to fast iterative solvers. The analysis results are supported by a range of numerical examples that demonstrate rates of convergence, and which show computational efficiency gains over a full hybridized formulation.