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 error 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 and coarsening. In this way, very economical and highly localized 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 of a posteriori error estimation, test the quality of the error estimator and the efficiency of the meshes by some numerical examples.



Ralf Hartmann
2000-03-31