@article{ Repin2010a,
  abstract = {We present guaranteed, robust and computable a posteriori error estimates for nonconforming approximations of elliptic problems. Our analysis is based on a Helmholtz-type decomposition of the error expressed in terms of fluxes. Such a decomposition results in a gradient term and a divergence-free term, that are the exact solutions of two auxiliary problems. We suggest a new approach to deriving computable two-sided bounds of the norms of these solutions. The a posteriori estimates obtained in this paper differ from those that are based on projections of nonconforming approximations to a conforming space. Numerical experiments confirm that these new estimates provide very accurate error bounds, and can be efficiently exploited in practical computations.},
  author = {Repin, S. I. and Tomar, S. K.},
  doi = {10.1093/imanum/drp037},
  issn = {0272-4979},
  journal = {IMA Journal of Numerical Analysis},
  month = {February},
  number = {2},
  pages = {597--615},
  title = {{Guaranteed and robust error bounds for nonconforming approximations of elliptic problems}},
  url = {http://imajna.oxfordjournals.org/content/31/2/597#},
  volume = {31},
  year = {2010}
}

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