Two other methods, the * p* and the * hp* methods, have been
found, in most cases, to converge faster. The * p* method of refinement
requires that one increase the order of the basis function that was used to
represent the interpolation (i.e. linear to quadratic to cubic, etc.).
The * hp* method is a combination of the * h* and * p* methods and
has recently been shown to converge the fastest of the three methods
(but, as you might imagine, it is the hardest to implement). Take a minute to
estimate the number of additional elements that will be added for each
iteration and the total number of elements for say, five iterations of the
adaptive algorithm. Remember that this is a two-dimensional problem and
that the data you are working with is only one of 116 such MRI sections.
You should be able to get an idea of how the size of the problem increases
with accuracy. Obviously, due to limited CPU, memory, and time, one has to
make some choices concerning accuracy versus computational costs. One
possible practical solution to this problem is to calculate the number of
nodes that your particular workstation can handle and then refine only up
to that particular number.

(See exercise 8.)