ISBN 978-3-86853-878-6

978-3-86853-878-6, Reihe Mathematik

Roland Schäfer
Adaptive Multiresolution Discontinuous Galerkin Schemes for Conservation Laws

165 Seiten, Dissertation Rheinisch-Westfälische Technische Hochschule Aachen (2011), Softcover, B5

Zusammenfassung / Abstract

In this work we introduce an adaptive multiresolution discontinuous Galerkin scheme for conservation laws. The central idea is to accelerate the computation of a given Discontinuous Galerkin scheme. This is achieved by coarsening the uniform reference grid via wavelet coefficient thresholding and performing evolution of the data on the resulting adaptive grid. This introduces a small error in each time step. To control this error, the grid for the next time step has to be predicted from the current data. We develop a prediction strategy that allows us to verify the boundedness of the perturbation error introduced by thresholding. Numerical tests confirm the analytical results. Further modifications to this h-adaptive scheme are described, analyzed and tested.