Hybridized Discontinuous Galerkin Discretizations for Flow Problems

Discontinuous Galerkin methods have several properties that make them attractive for the simulation of fluid flow: � Mimic physical directionality in transport problems: Fluxes into and out of the cells balanced (generalization of finite volumes to high order) � Work well also for convection-dominated problems, as opposed to continuous FEM which need stabilization � Can easily couple non-conforming grids together � Stable approximation with standard polynomial spaces However, their cost is typically higher than continuous FEM or finite volumes (more degrees of freedom, wider stencils). Hybridized discontinuous Galerkin (HDG) methods try to mitigate this cost disadvantage by reducing the final linear problem to degrees of freedom on element faces.