A Note on Constant-Free A Posteriori Error Estimates

Authors:
R. Verfürth
Affiliations:
ruediger.verfuerth@ruhr-uni-bochum.de
Venue:
SIAM Journal on Numerical Analysis
Year:
2009

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Abstract

In this note we look at constant-free a posteriori error estimates from a different perspective. We show that they can be interpreted as an alternative way of expressing the residual of a finite element approximation and thus fit into the same framework as other a posteriori error estimates such as residual error indicators. Our approach also reveals that, when applied to singularly perturbed reaction-diffusion or convection-diffusion problems, constant-free a posteriori error estimates will not be fully robust unless extra measures are taken.