Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations
Journal of Computational Physics
A high-order discontinuous Galerkin method for the unsteady incompressible Navier-Stokes equations
Journal of Computational Physics
A Note on Discontinuous Galerkin Divergence-free Solutions of the Navier-Stokes Equations
Journal of Scientific Computing
hpGEM---A software framework for discontinuous Galerkin finite element methods
ACM Transactions on Mathematical Software (TOMS)
An Augmented Lagrangian-Based Approach to the Oseen Problem
SIAM Journal on Scientific Computing
A space--time discontinuous Galerkin method for the time-dependent Oseen equations
Applied Numerical Mathematics
An Equal-Order DG Method for the Incompressible Navier-Stokes Equations
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
To CG or to HDG: A Comparative Study
Journal of Scientific Computing
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We introduce a space-time discontinuous Galerkin (DG) finite element method for the incompressible Navier-Stokes equations. Our formulation can be made arbitrarily high-order accurate in both space and time and can be directly applied to deforming domains. Different stabilizing approaches are discussed which ensure stability of the method. A numerical study is performed to compare the effect of the stabilizing approaches, to show the method's robustness on deforming domains and to investigate the behavior of the convergence rates of the solution. Recently we introduced a space-time hybridizable DG (HDG) method for incompressible flows [S. Rhebergen, B. Cockburn, A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains, J. Comput. Phys. 231 (2012) 4185-4204]. We will compare numerical results of the space-time DG and space-time HDG methods. This constitutes the first comparison between DG and HDG methods.