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Refinement Strategy

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 [24] adopted in this study. The permissible value of the error per element is calculated as


where is the total number of elements and is the prescribed relative permissible error. 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


Assuming the rate of the convergence of the error to be , where stands for the degree of the interpolation polynomial, the predicted (de)refined element size reads


Of course, this simple convergence rule is not valid near singularities, where more progressive refinement, related to the intensity of the singularity, is desirable.

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Daniel Rypl