Abstract
We present an approach to solving conservation equations by the adaptive discontinuous Galerkin finite element method (DG method). Using a global duality argument and Galerkin orthogonality, we obtain a residual-based representation for the error with respect to an arbitrary functional of the solution. This results in local indicators that can be evaluated numerically and which are used for adaptive mesh refinement. In this way, very economical meshes can be generated which are tailored to the cost-efficient computation of the quantity of interest. We demonstrate the main ingredients of this approach to a posteriori error estimation and test the quality of the error estimator and the efficiency of the meshes by some numerical examples.
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Hartmann, R. (2001). Adaptive Fe Methods for Conservation Equations. In: Freistühler, H., Warnecke, G. (eds) Hyperbolic Problems: Theory, Numerics, Applications. ISNM International Series of Numerical Mathematics, vol 141. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8372-6_3
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DOI: https://doi.org/10.1007/978-3-0348-8372-6_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9538-5
Online ISBN: 978-3-0348-8372-6
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