The error in energy, measured by the energy norm, is defined in general as [42,43,44],
where 
and L is the differential operator for
the governing differential equation (i.e. it contains the derivatives
operating on 
and any function multiplying 
). For physical
problems this is often associated with the energy density.
Another common measure of convergence utilizes the 
norm. This can
be termed the average error and can be associated with errors in any
quantity. The 
norm is defined as,
