Hybrid Discontinuous Galerkin methods with relaxed H (div)-conformity for incompressible flows: Part II

Philip L. Lederer, Christoph Lehrenfeld*, Joachim Schöberl

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

16 Citations (Scopus)


The present work is the second part of a pair of papers, considering Hybrid Discontinuous Galerkin methods with relaxed H(div)-conformity. The first part mainly dealt with presenting a robust analysis with respect to the mesh size h and the introduction of a reconstruction operator to restore divergence-conformity and pressure robustness (pressure independent velocity error estimates) using a modified force discretization. The aim of this part is the presentation of a high order polynomial robust analysis for the relaxed H(div)-conforming Hybrid Discontinuous Galerkin discretization of the two dimensional Stokes problem. It is based on the recently proven polynomial robust LBB-condition for BDM elements, Lederer and Schöberl (IMA J. Numer. Anal. (2017)) and is derived by a direct approach instead of using a best approximation Céa like result. We further treat the impact of the reconstruction operator on the hp analysis and present a numerical investigation considering polynomial robustness. We conclude the paper presenting an efficient operator splitting time integration scheme for the Navier-Stokes equations which is based on the methods recently presented in Lehrenfeld and Schöberl (Comp. Methods Appl. Mech. Eng. 307 (2016) 339-361) and includes the ideas of the reconstruction operator.

Original languageEnglish
Pages (from-to)503-522
Number of pages20
JournalESAIM: Mathematical Modelling and Numerical Analysis
Issue number2
Publication statusPublished - 1 Mar 2019
Externally publishedYes


  • H(div)-conforming finite elements
  • High order methods
  • Hybrid Discontinuous Galerkin methods
  • Pressure robustness
  • Stokes equations
  • n/a OA procedure


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