Error Estimation and Adaptation in Hybridized Discontinuous Galerkin Methods

rst- and second-order systems of conservation laws. A discrete adjoint solution is obtained by a Schurcomplement solver similar to that used in the primal problem. An error estimate is obtained by computing the adjoint on an enriched solution space that consists of uniform order renement of both the element and the face approximations. The error is given by the adjoint-weighted residual, the localized contributions of which provide an adaptive error indicator for hanging-node h-renement. Results for inviscid, laminar, and Reynolds-averaged turbulent compressible Navier-Stokes simulations in two and three dimensions demonstrate some of the potential gains of output-based adaptivity for hybridized discontinuous Galerkin discretizations.