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6.0.2 Energy Norms     continued...

While the norms given above are defined on the whole domain, one can note that the square of each can be obtained by summing element contributions,

where i represents an element contribution and m the total element number. Often for an optimal finite element mesh, one tries to make the contributions to this square of the norm equal for all elements.

While the absolute values given by the energy or norms have little value, one can construct a relative percentage error that can be more readily interpreted:

This quantity, in effect, represents a weighted RMS error. The analysis can be determined for the whole domain or for element subdomains. One can use it in an adaptive algorithm by checking element errors against some predefined tolerance, , and increasing the DOF only those areas which are above the predefined tolerance.