A posteriori error analysis for numerical approximations of Friedrichs systems
An a posteriori error analysis for numerical approximations of Friedrichs systems is presented. The global error is decomposed into a locally created part and a propagating component. Residual-based two-sided local a posteriori error bounds are derived for the locally created part of the global error. These suggest taking the \(L^{2}\)-norm as well as weaker, dual norms of the computable residual as local error indicators. The dual graph norm of the residual \({\mathbf r}_{h}\) is further bounded from above and below in terms of the \(L^{2}\) norm of \(h{\mathbf r}_{h}\) where \(h\) is the local mesh size. The theoretical results are illustrated by a series of numerical experiments.
scientific article; zbMATH DE number 1356178