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,