Error estimation and adaptive mesh refinement for aerodynamic flows
Hartmann, Ralf and Houston, Paul (2009) Error estimation and adaptive mesh refinement for aerodynamic flows. In: Proceedings of the 36THCFD/Adigma course on HP-adaptive and HP-multigrid methods. von Karman Institute for Fluid Dynamics, Rhode Saint Genèse, Belgium. ISBN 978-2-930389-98-2 (In Press)
Official URL: http://www.vki.ac.be/
This lecture course covers the theory of so-called duality-based a posteriori error estimation of DG finite element methods. In particular, we formulate consistent and adjoint consistent DG methods for the numerical approximation of both the compressible Euler and Navier-Stokes equations; in the latter case, the viscous terms are discretized based on employing an interior penalty method. By exploiting a duality argument, adjoint-based a posteriori error indicators will be established. Moreover, application of these computable bounds within automatic adaptive finite element algorithms will be developed. Here, a variety of isotropic and anisotropic adaptive strategies, as well as $hp$-mesh refinement will be investigated.
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