Geodesic
Functional a posteriori error estimates for the
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 38, Tome 348 (2007), pp. 127-146

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In this paper, a general form of functional type a posteriori error estimates for linear reaction-convection-diffusion problems is presented. It is derived by purely functional arguments without attracting specific properties of the approximation method. The estimate provides a guaranteed upper bound of the difference between the exact solution and any conforming approximation from the energy functional class. It is also proved that the derived error majorants give computable quantities which are equivalent to the error evaluated in the energy and combined primal-dual norms. 
@article{ZNSL_2007_348_a4,
     author = {S. Nicaise and S. I. Repin},
     title = {Functional a posteriori error estimates for the},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {127--146},
     publisher = {mathdoc},
     volume = {348},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_348_a4/}
}
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S. Nicaise; S. I. Repin. Functional a posteriori error estimates for the. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 38, Tome 348 (2007), pp. 127-146. http://geodesic.mathdoc.fr/item/ZNSL_2007_348_a4/