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