A posteriori error analysis for numerical approximations of Friedrichs systems

The global error of numerical approximations for symmetric positive systems in the sense of Friedrichs 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 rh is further bounded from above and below in terms of the L-2 norm of hr(h) where r(h) is the local mesh size. The theoretical results are illustrated by a series of numerical experiments.Mathematics Subject Classification (1991): 65M15, 65M50, 65M60.