Adjoint-based hp-adaptation for a class of high-order hybridized finite element schemes for compressible flows
We present a robust and effcient hp-adaptation methodology, building on a class of hybridized finite element schemes for (nonlinear) convection-diffusion problems, including compressible Euler and Navier-Stokes equations. Using a discrete-adjoint approach, sensitivities with respect to output functionals of interest are computed to drive the adaptation. The theoretical framework is embedded in a unified formulation of a large class of hybridized, adjoint consistent schemes. 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 some smoothness indicators. Numerical results are shown for a scalar convection-diffusion case, and also inviscid subsonic, transonic, and laminar flow around the NACA0012 airfoil to demonstrate the viability of the hp-adaptivity in reducing the error in the target functional. © 2013 by Aravind Balan.
