École Nationale Supérieure de
Techniques Avancées

Abstract

The goal of this study was to find a robust and computationally efficient technique of H(div)-conforming flux reconstruction on polyhedral meshes in 3D. The reconstruction devised by Cheng et al. preserving constant divergence at the discrete level was chosen for the implementation. Some modifications of the algorithm were added in order to guarantee the P0-consistency of the reconstruction and to increase computational efficiency. This modified reconstruction was compared to existing nonconforming operators on a series of numerical tests. To our knowledge, it is the first implementation of the Cheng-like algorithm in 3D.