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.
