The hphp-adaptive FEM based on continuous Sobolev embeddings: Isotropic refinements

The aim of this paper is to present a new class of smoothness testing strategies in the context of hphp-adaptive refinements based on continuous Sobolev embeddings. In addition to deriving a modified form of the 1d smoothness indicators introduced in  [26], they will be extended and applied to a higher dimensional framework. A few numerical experiments in the context of the hphp-adaptive FEM for a linear elliptic PDE will be performed.