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
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)
Journal of Computational Physics
Journal of Computational Physics
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
SIAM Journal on Scientific Computing
Journal of Computational Physics
A Hybridizable and Superconvergent Discontinuous Galerkin Method for Biharmonic Problems
Journal of Scientific Computing
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems
SIAM Journal on Scientific Computing
Hybridizable Discontinuous Galerkin Methods for Timoshenko Beams
Journal of Scientific Computing
A Comparison of HDG Methods for Stokes Flow
Journal of Scientific Computing
Journal of Computational Physics
High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics
Journal of Computational Physics
Journal of Computational Physics
A space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
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We present the first space-time hybridizable discontinuous Galerkin (HDG) finite element method for the incompressible Navier-Stokes and Oseen equations. Major advantages of a space-time formulation are its excellent capabilities of dealing with moving and deforming domains and grids and its ability to achieve higher-order accurate approximations in both time and space by simply increasing the order of polynomial approximation in the space-time elements. Our formulation is related to the HDG formulation for incompressible flows introduced recently in, e.g., [N.C. Nguyen, J. Peraire, B. Cockburn, A hybridizable discontinuous Galerkin method for Stokes flow, Comput. Methods Appl. Mech. Eng. 199 (2010) 582-597]. However, ours is inspired in typical DG formulations for compressible flows which allow for a more straightforward implementation. Another difference is the use of polynomials of fixed total degree with space-time hexahedral and quadrilateral elements, instead of simplicial elements. We present numerical experiments in order to assess the quality of the performance of the methods on deforming domains and to experimentally investigate the behavior of the convergence rates of each component of the solution with respect to the polynomial degree of the approximations in both space and time.