To randomly add to this discussion... In general higher order polynomials are good for approximating smooth functions, such as the tail of an exponential decay. Interestingly, a denser grid with lower order polynomials sometimes works better for approximating a function that oscillates rapidly, such as the peak of a tightly packed sinosoidal wave.
Think what would happen if you try to represent a zero valued function on one element. The order of the interpolation does not affect the accuracy its approximation! Then try to map an exponentially decaying function with increasing polynomial order and see what happens... That is a good exercise for a rainy day or a sunday afternoon. :-) Maybe try to approximate the functions, x, x^2, ..., x^n??? The result is, that if you want to save dofs, and your solution is mixed, hp-adaptivity is definately worth exploring - and it is alot of fun! That's my penny worth. :-) Best, Toby -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
