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 b
ounds are derived for the locally created part of the global error. These s
uggest 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) w
here r(h) is the local mesh size. The theoretical results are illustrated b
y a series of numerical experiments.Mathematics Subject Classification (199
1): 65M15, 65M50, 65M60.