Error estimation and hp–adaptive mesh refinement for discontinuous Galerkin methods

Abstract

We present adjoint-based techniques to estimate the error of a numerical flow solution with respect to a given target quantity like an aerodynamic force coefficient. This estimate can be used to judge the overall accuracy of a computation, to enhance the computed value of the target quantity and to drive a solution-adaptive mesh refinement process. The error estimation procedure is extended to multiple target quantities. The discontinuous ansatz spaces of the DG discretization allow for both element subdivision as well as a local increase of polynomial degrees for increasing the flow resolution. Targeting optimal rates of convergence, a smoothness estimation based on a truncated Legendre series expansion of the solution is employed to locally select the more promising strategy. Numerical examples for inviscid, laminar viscous and turbulent viscous flows demonstrate the efficiency of the proposed algorithms.