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zienkiewicz

hi all,

i would like to know how can i find the error in a heat transfer problem with the help of

zienkiewicz zhu error estimator.

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The first step is of course to read the very clearly written papers by Zienkiewicz and Zhu:

  1. O.C. Zienkiewicz, J.Z. Zhu, A simple error estimator and adaptive procedure for practical engineering analysis, Int. J. Numer. Methods Eng. 24 (1987) 337-357.
  2. O.C. Zienkiewicz, J.Z. Zhu, The superconvergent patch recovery and a posteriori error estimates. Part 1: the recovery technique, Int. J. Numer. Methods Eng. 33 (1992) 1331-1364.
  3. O.C. Zienkiewicz, J.Z. Zhu, The superconvergent patch recovery and a posteriori error estimates. Part 2: error estimates and adaptivity, Int. J. Numer. Methods Eng. 33 (1992) 1365-1382.

In solid mechanics, the ZZ error estimate is usually written as

error = σ* - σ

where σ* is the recovered stress at the nodes using the procedure explained in paper 2 above.  For heat conduction problems the stress is replaced with the heat flux q = - k grad T and the same procedure can be applied.  Then the error is given by

error = q* - q

The value of q witl be given by the temperature field that you solve for.  q* can be obtained by the superconvergent patch recovery technique. 

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