Measures of convergence often depend on how the closeness of
measuring the distance between functions is defined. Another common
description of measuring convergence is, uniform convergence, which
requires that the maximum value of 
in the
domain vanish as 
. This is stronger than pointwise
convergence as it requires a unform rate of convergence at every point in
the domain. Two other commonly used measures are convergence in
energy and convergence in mean, which involve measuring an
average of a function of the pointwise error over the domain [45].
In general, proving pointwise convergence is very difficult except in the
simplest cases, while proving the convergence of an averged value, such as
energy, is often easier. Of course, scientists and engineers are often much
more interested in assuring that their answers are accurate in a pointwise
sense than an energy sense because they typically want to know
values of the solution 
and graidents, 
at specific
places.
