The first step is of course to read the very clearly written papers by Zienkiewicz and Zhu:
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.
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.
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.
Re: ZZ error estimator for heat transfer
The first step is of course to read the very clearly written papers by Zienkiewicz and Zhu:
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.