Geodesic
A~posteriori error estimates for approximate solutions of variational problems with power growtn functionals
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 29, Tome 249 (1997), pp. 244-255

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The present paper is concerned with the derivation of upper estimates of the difference $\|v-u\|$ where $u$ is a minimizer of a variational problem and $v$ is an element of the corresponding functional space. By using methods of duality theory, we derive a majorizing functional, which explicitly depends only on $v$ and the data of the problem. The advantage of this majorant is that it does not contain unknown constants and can be directly computed by simple numerical methods. 
@article{ZNSL_1997_249_a11,
     author = {S. I. Repin},
     title = {A~posteriori error estimates for approximate solutions of variational problems with power growtn functionals},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {244--255},
     publisher = {mathdoc},
     volume = {249},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_249_a11/}
}
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S. I. Repin. A~posteriori error estimates for approximate solutions of variational problems with power growtn functionals. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 29, Tome 249 (1997), pp. 244-255. http://geodesic.mathdoc.fr/item/ZNSL_1997_249_a11/