HDG-NEFEM with Degree Adaptivity for Stokes Flows

This paper presents the first degree adaptive procedure able to directly use the geometry given by a CAD model. The technique uses a hybridisable discontinuous Galerkin discretisation combined with a NURBS-enhanced rationale, completely removing the uncertainty induced by a polynomial approximation of curved boundaries that is common within an isoparametric approach. The technique is compared against two strategies to perform degree adaptivity currently in use. This paper demonstrates, for the first time, that the most extended technique for degree adaptivity can easily lead to a non-reliable error estimator if no communication with CAD software is introduced whereas if the communication with the CAD is done, it results in a substantial computing time. The proposed technique encapsulates the CAD model in the simulation and is able to produce reliable error estimators irrespectively of the initial mesh used to start the adaptive process. Several numerical examples confirm the findings and demonstrate the superiority of the proposed technique. The paper also proposes a novel idea to test the implementation of high-order solvers where different degrees of approximation are used in different elements