An hp-adaptive strategy based on continuous Sobolev embeddings

A new hp-adaptive approach for finite element methods is presented. Specifically, the paper addresses the well-known question of how to effectively decide between h- and p-refinement within an adaptive hp-finite element procedure. The main idea is based on testing the smoothness of the underlying PDE solution by means of suitable continuous Sobolev embeddings. Numerical experiments confirm the effectiveness of the proposed method.