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,