Error Estimation and Adaptation in Hybridized Discontinuous Galerkin Methods

摘要

This paper presents an output-based error estimation and adaptation strategy for hybridized discontinuous Galerkin discretizations of first- and second-order systems of conservation laws. A discrete adjoint solution is obtained by a Schur-complement 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 refinement 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-refinement. Results for in-viscid, 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.