Analysis of non-conforming DPG methods on polyhedral meshes using fractional Sobolev norms

摘要

The work is concerned with two problems: (a) analysis of a discontinuous Petrov-Galerkin (DPG) method set up in fractional energy spaces, (b) use of the results to investigate a non-conforming version of the DPG method for general polyhedral meshes. We use the ultraweak variational formulation for the model Laplace equation. The theoretical estimates are supported with 3D numerical experiments. (C) 2020 Elsevier Ltd. All rights reserved.