Journal of Mathematical Sciences

, Volume 170, Issue 4, pp 554–566 | Cite as

A posteriori error estimates for approximations of evolutionary convection–diffusion problems

  • S. I. Repin
  • S. K. Tomar

We derive computable upper bounds for the difference between an exact solution of the evolutionary convection-diffusion problem and an approximation of this solution. The estimates are obtained by certain transformations of the integral identity that defines the generalized solution. These estimates depend on neither special properties of the exact solution nor its approximation and involve only global constants coming from embedding inequalities. The estimates are first derived for functions in the corresponding energy space, and then possible extensions to classes of piecewise continuous approximations are discussed. Bibliography: 7 titles.


Radon Steklov Institute Integral Identity Posteriori Error Estimate Young Inequality 
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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.V. A. Steklov Institute of MathematicsRussian Academy of SciencesSt. PetersburgRussia
  2. 2.Johann Radon Institute for Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria

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