Analysis of a hybridized/interface stabilized finite element method for the stokes equations

© 2017 Society for Industrial and Applied Mathematics. Stability and error analysis of a hybridized discontinuous Galerkin finite element method for Stokes equations is presented. The method is locally conservative, and for particular choices of spaces the velocity field is point-wise solenoidal. It is shown that the method is inf-sup stable for both equal-order and locally Taylor-Hood-type spaces, and a priori error estimates are developed. The considered method can be constructed to have the same global algebraic structure as a conforming Galerkin method, unlike standard discontinuous Galerkin methods that have a greater number of degrees of freedom than conforming Galerkin methods on a given mesh. We assert that this method is among the simplest and most exible finite element approaches for Stokes ow that provide local mass conservation. With this contribution the mathematical basis is established, and this supports the performance of the method that has been observed experimentally in other works