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

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 $H({\rm div})$-conforming velocity field, pointwise satisfaction of the continuity equation and \emph{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.

💡 Research Summary

This paper introduces and rigorously analyzes a novel finite‑element discretization for the incompressible Stokes equations, called the embedded‑hybridized discontinuous Galerkin (EDG‑HDG) method. The Stokes problem under consideration is the standard formulation
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