Natural hierarchical refinement for finite element methods

Current formulations of adaptive nite element mesh re nement seem simple enough, but their implementations prove to be a formidable task. We o er an alternative point of departure which yields equivalent adapted approximation spaces wherever the traditional mesh re nement is applicable, but our method proves to be signi cantly simpler to implement. At the same time it is much more powerful in that it is general (no special tricks are required for di erent types of nite elements), and applicable for some newer approximations where traditional mesh re nement concepts are not of much help, for instance on subdivision surfaces