Hi
If you have Lagrange/Serendipity-elements then what is used is the elements in the mesh file. All shapes are supported to 2nd degree, some shapes even up to 4th.
More convenient way to increase basis power is to use hierarchical p-basis. This does not work for all solvers, but does for HeatSolveVec, for example. There you can say
where n defines the polynomial degree. Usually n=2..4 but it could be at least 10 (which is usually an overkill).
For curved shapes you may have to pull some additional keywords to obtain ideal convergence rate.
-Peter