A posteriori error analysis for numerical approximations of Friedrichs systems

Abstract.

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 ${\vec r}_h$ is further bounded from above and below in terms of the $L^2$ norm of $h {\vec r}_h$ where h is the local mesh size. The theoretical results are illustrated by a series of numerical experiments.