## What is/are Hybridized Discontinuous?

Hybridized Discontinuous - We present a hybridized discontinuous Galerkin (HDG) method for stationary linearized incompressible magnetohydrodynamics (MHD) equations.^{[1]}For illustration purposes, the non-modal analysis is applied to the hybridized discontinuous Galerkin methods as representatives of SEM.

^{[2]}In this paper, a hybridized discontinuous Galerkin time domain method consisting of interior penalty discontinuous Galerkin (IPDG) time domain based on Helmholtz vector wave equation and discontinuous Galerkin time domain (DGTD) method based on Maxwell’s equations has been developed to solve the multiscale problems.

^{[3]}We perform extensive numerical studies with hybridized mixed methods, hybridized discontinuous Galerkin method, weak Galerkin method, and a hybridized version of interior penalty discontinuous Galerkin methods on a range of elliptic problems including subsurface flow through highly heterogeneous porous media.

^{[4]}A combined discontinuous Galerkin method across space--time slabs, and space--time hybridized discontinuous Galerkin method within a space--time slab, results in an approximate velocity field that is $H({\rm div})$-conforming and exactly divergence-free, even on time-dependent domains.

^{[5]}By combining concepts from particle-in-cell (PIC) and hybridized discontinuous Galerkin (HDG) methods, we present a particle–mesh scheme for flow and transport problems which allows for diffusion-free advection while satisfying mass and momentum conservation – locally and globally – and extending to high-order spatial accuracy.

^{[6]}We introduce a hybridized discontinuous Galerkin method for the incompressible Reynolds Averaged Navier-Stokes equations coupled with the Spalart-Allmaras one equation turbulence model.

^{[7]}We present well-posedness and an a priori error analysis of the hybridized discontinuous Galerkin method for the stationary form of the Navier–Stokes problem proposed in Rhebergen and Wells (J Sci Comput 76(3):1484–1501, 2018.

^{[8]}We develop a high-order hybridized discontinuous Galerkin (HDG) method for a linear degenerate elliptic equation arising from a two-phase mixture of mantle convection or glacier dynamics.

^{[9]}

## hybridized discontinuous galerkin

We present a hybridized discontinuous Galerkin (HDG) method for stationary linearized incompressible magnetohydrodynamics (MHD) equations.^{[1]}For illustration purposes, the non-modal analysis is applied to the hybridized discontinuous Galerkin methods as representatives of SEM.

^{[2]}In this paper, a hybridized discontinuous Galerkin time domain method consisting of interior penalty discontinuous Galerkin (IPDG) time domain based on Helmholtz vector wave equation and discontinuous Galerkin time domain (DGTD) method based on Maxwell’s equations has been developed to solve the multiscale problems.

^{[3]}We perform extensive numerical studies with hybridized mixed methods, hybridized discontinuous Galerkin method, weak Galerkin method, and a hybridized version of interior penalty discontinuous Galerkin methods on a range of elliptic problems including subsurface flow through highly heterogeneous porous media.

^{[4]}A combined discontinuous Galerkin method across space--time slabs, and space--time hybridized discontinuous Galerkin method within a space--time slab, results in an approximate velocity field that is $H({\rm div})$-conforming and exactly divergence-free, even on time-dependent domains.

^{[5]}By combining concepts from particle-in-cell (PIC) and hybridized discontinuous Galerkin (HDG) methods, we present a particle–mesh scheme for flow and transport problems which allows for diffusion-free advection while satisfying mass and momentum conservation – locally and globally – and extending to high-order spatial accuracy.

^{[6]}We introduce a hybridized discontinuous Galerkin method for the incompressible Reynolds Averaged Navier-Stokes equations coupled with the Spalart-Allmaras one equation turbulence model.

^{[7]}We present well-posedness and an a priori error analysis of the hybridized discontinuous Galerkin method for the stationary form of the Navier–Stokes problem proposed in Rhebergen and Wells (J Sci Comput 76(3):1484–1501, 2018.

^{[8]}We develop a high-order hybridized discontinuous Galerkin (HDG) method for a linear degenerate elliptic equation arising from a two-phase mixture of mantle convection or glacier dynamics.

^{[9]}