The refinement strategy is usually based on the assumption that the error is distributed uniformly over all elements. This is also the case for the ZZ (Zienkiewicz-Zhu) refinement approach [5] adopted in this study. Since the error is in fact computed on each element of the coarse problem (by summing contributions from underlying elements of the reference mesh) then the need of (de)refinement may be quantified by the ratio of the actual error and the user prescribed limit error. In fact, in the case of linear elements, the inverse value of this ratio directly determines the rate of (de)refinement.

*Daniel Rypl
2005-12-03*