We present a comparison between hybridized and non-hybridized discontinuous Galerkin methods in the context of target-based hp-adaptation. Using a discrete-adjoint approach, sensitivities with respect to output functionals are computed to drive the adaptation. From the error distribution given by the adjoint-based error estimator, h-or p-refinement is chosen based on the smoothness of the solution which can be quantified by properly-chosen smoothness indicators. Numerical results are shown for inviscid subsonic and transonic, and laminar viscous flow around the NACA0012 airfoil.

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We present a robust and efficient target-based mesh adaptation methodology, building on hybridized discontinuous Galerkin schemes for (nonlinear) convection-diffusion problems, including the compressible Euler and Navier-Stokes equations. Hybridization of finite element discretizations has the main advantage, that the resulting set of algebraic equations has globally coupled degrees of freedom only on the skeleton of the computational mesh. Consequently, solving for these degrees of freedom involves the solution of a potentially much smaller system. This not only reduces storage requirements, but also allows for a faster solution with iterative solvers. The mesh adaptation is driven by an error estimate obtained via a discrete adjoint approach. Furthermore, the computed target functional can be corrected with this error estimate to obtain an even more accurate value. The aim of this paper is twofold: Firstly, to show the superiority of adjoint-based mesh adaptation over uniform and residual-based mesh refinement, and secondly to investigate the efficiency of the global error estimate.

We present an efficient adaptation methodology on anisotropic meshes for the recently developed hybridized discontinuous Galerkin scheme for (nonlinear) convection-diffusion problems, including compressible Euler and Navier-Stokes equations. The methodology extends the refinement strategy of Dolejsi [8] based on an interpolation error estimate to incorporate an adjoint-based error estimate. For each element, we set the area using the adjoint-based error estimate, and we seek the anisotropy, of the element, which gives the smallest interpolation error in the L q -norm (q ∈ [1, ∞)). For hp-adaptation, the local polynomial degree is also chosen in such a way that the configuration -element shape and the polynomial degree, gives the smallest interpolation error in the L q -norm. Numerical results are shown for a scalar convection-diffusion case with a strong boundary layer, as well as for inviscid subsonic, transonic and supersonic and viscous subsonic flow around the NACA0012 airfoil, to demonstrate the effectiveness of the adaptation methodology.