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.
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Received January 10, 1997 / Revised version received March 5, 1998
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Houston, P., Mackenzie, J., Süli, E. et al. A posteriori error analysis for numerical approximations of Friedrichs systems. Numer. Math. 82, 433–470 (1999). https://doi.org/10.1007/s002110050426
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DOI: https://doi.org/10.1007/s002110050426