Divergence-conforming HDG methods for Stokes flows

B Cockburn, FJ Sayas - Mathematics of Computation, 2014 - ams.org
In this paper, we show that by sending the normal stabilization function to infinity in the
hybridizable discontinuous Galerkin methods previously proposed in [Comput. Methods …

Devising HDG methods for Stokes flow: an overview

B Cockburn, K Shi - Computers & Fluids, 2014 - Elsevier
We provide a short overview of our recent work on the devising of hybridizable
discontinuous Galerkin (HDG) methods for the Stokes equations of incompressible flow …

Hybrid discontinuous Galerkin methods with relaxed H (div)-conformity for incompressible flows. Part I

PL Lederer, C Lehrenfeld, J Schöberl - SIAM Journal on Numerical Analysis, 2018 - SIAM
We propose a new discretization method for the Stokes equations. The method is an
improved version of the method recently presented in C. Lehrenfeld and J. Schöberl …

Analysis of a hybridizable discontinuous Galerkin method for the steady-state incompressible Navier-Stokes equations

A Cesmelioglu, B Cockburn, W Qiu - Mathematics of Computation, 2017 - ams.org
We present the first a priori error analysis of the hybridizable discontinuous Galerkin method
for the approximation of the Navier-Stokes equations proposed in J. Comput. Phys. vol. 230 …

A note on the devising of superconvergent HDG methods for Stokes flow by M-decompositions

B Cockburn, G Fu, W Qiu - IMA Journal of Numerical Analysis, 2017 - academic.oup.com
In this article, we to devise superconvergent hybridizable discontinuous Galerkin methods
on unstructured polygonal/polyhedral meshes for the Stokes equations of incompressible …

A superconvergent HDG method for the incompressible Navier–Stokes equations on general polyhedral meshes

W Qiu, K Shi - IMA Journal of Numerical Analysis, 2016 - academic.oup.com
We present a superconvergent hybridizable discontinuous Galerkin method for the steady-
state incompressible Navier–Stokes equations on general polyhedral meshes. For an …

Analysis of HDG methods for Stokes flow

B Cockburn, J Gopalakrishnan, N Nguyen… - Mathematics of …, 2011 - ams.org
In this paper, we analyze a hybridizable discontinuous Galerkin method for numerically
solving the Stokes equations. The method uses polynomials of degree $ k $ for all the …

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

PL Lederer, C Lehrenfeld, J Schöberl - … Modelling and Numerical …, 2019 - esaim-m2an.org
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 hybridizable discontinuous Galerkin method for Stokes flow

NC Nguyen, J Peraire, B Cockburn - Computer Methods in Applied …, 2010 - Elsevier
In this paper, we introduce a hybridizable discontinuous Galerkin method for Stokes flow.
The method is devised by using the discontinuous Galerkin methodology to discretize a …

A staggered discontinuous Galerkin method for the Stokes system

HH Kim, ET Chung, CS Lee - SIAM Journal on Numerical Analysis, 2013 - SIAM
Discontinuous Galerkin (DG) methods are a class of efficient tools for solving fluid flow
problems. There are in the literature many greatly successful DG methods. In this paper, a …