[1]
Reed, W.H., Hill, T.R., Triangular mesh methods for the neutron transport equation, Los Alamos Scientific Laboratory Report, LA-UR-73-479, 1973.

[2]
Cockburn, B., Hou, S., Shu, C.-W., TVD Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case, Mathematics of Computation, 55(1990), pp. 545–581.

[3]
Cockburn, B., Shu, C.-W., The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional system, J. Comput. Phys., 141(1998), pp. 199–224.

[4]
Luo, H., Baum, J.D., Löhner, R., A discontinuous Galerkin method based on a Taylor basis for the compressible flows on arbitrary grids, J. Comput. Phys., 227(2008), pp. 8875–8893.

[5]
Luo, H., Luo, L.Q., Nourgaliev, R., Mousseau, V.A., Dinh, N., A reconstructed discontinuous Galerkin method for the compressible Navier-Stokes equations on arbitrary grids, J. Comput. Phys., 229(2010), pp. 6961–6978.

[6]
van Leer, B., Nomura, S., Discontinuous Galerkin method for Diffusion, AIAA-2005-5108.

[7]
van Leer, B., Lo, M., A discontinuous Galerkinmethod for diffusion based on recovery, AIAA-2007-4083.

[8]
Liu, H.L., Yan, J., The direct discontinuous Galerkin (DDG) methods for diffusion problems
SIAM J. Numer. Anal., 47(2009), pp. 675–698.

[9]
Liu, H.L., Yan, J., The direct discontinuous Galerkin (DDG) method for diffusion with interface corrections, Commun. Comput. Phys., 8(2010), pp. 541–564.

[10]
Kannan, R., Wang, Z.J., The direct discontinuous Galerkin (DDG) viscous flux scheme for the high order spectral volume method, Computers & Fluids, 39(2010), pp. 2007–2021.

[11]
Bassi, F., Rebay, S., Discontinuous Galerkin solution of the Reynolds-averaged Navier-Stokes and *k*–*w* turbulence model equations, Computers & Fluids, 34(2005), pp. 507–540.

[12]
Cockburn, B., Shu, C.-W., The local discontinuous Galerkin method for time dependent convection-diffusion systems, SIAM J. Numer. Anal., 35(1998), pp. 2440–2463.

[13]
Gao, H.Y., Wang, Z.J., Huynh, H.T., Differential formulation of discontinuous Galerkin and related methods for the Navier-Stokes equations, Commun. Comput. Phys., 13(2013), pp. 1013–1044.

[14]
Peraire, J., Persson, P.O., The compact discontinuous Galerkin (CDG) method for elliptic problems, SIAM J. Sci. Comput., 30(2008), pp. 1806–1824.

[15]
Bassi, F., Rebay, S., A high-order accurate discontinuous finite element method for the numerical solution of compressible Navier-Stokes equations, J. Comput. Phys., 131(1997), pp. 267–279.

[16]
Arnold, D.N., Brezzi, F., Cockburn, B., Marini, L.D., Unified analysis of discontinuous Galerkin methods fro elliptic problems, SIAM J. Numer. Anal., 19(2002), pp. 742–760.

[17]
Hartmann, R., Houston, P., An optimal order interior penalty discontinuous Galerkin discretization of the compressible Navier-Stokes equations, J. Comput. Phys., 227(2008), pp. 9670–9685.

[18]
Douglas, J., Dupont, T., Interior penalty procedures for eplliptic and parabolic Galerkin methods, in Computing Methods in Applied Sciences, Lecture Notes in Phys., Springer, Berlin, 1976, pp. 207–216.

[19]
Arnold, D.N., An interior penalty finite element method with discontinuous elements, SIAM J. Numer. Anal., 19(1982), pp. 742–760.

[20]
Wheeler, M.F., An elliptic collocation-finite element method with interior penalties, SIAM J. Numer. Anal., 15(1978), pp. 152–161.

[21]
Gassner, G., Löcher, F., Munz, C.-D., A contribution to the construction of diffusion fluxes for finite volume and discontinuous Galerkin schemes, J. Comput. Phys., 224(2207), pp. 1049–1063.

[22]
Luo, H., Baum, J.D., Löhner, R., A fast, matrix-free implicit method for compressible flows on unstructured grids, J. Comput. Phys., 146(1998), pp. 664–690.

[23]
Sun, Y., Wang, Z.J., Liu, Y., Spectral (finite) volume method for conservation laws on unstructured grids: extension to viscous flow, J. Comput. Phys., 215(2006), pp. 41–58.

[24]
Liu, Y., Vinokur, M., Wang, Z.J., Spectral (finite) volume method for conservation laws on unstructured grids V: extension to three-dimensional systems, J. Comput. Phys., 212(2006), pp. 454–472.

[25]
Luo, H., Xia, Y.D., Li, S.J., Nourgaliev, R., Cai, C.P., A Hermite WENO reconstruction-based discontinuous Galerkin method for the Euler equations on tetrahedral grids, J. Comput. Phys., 231(2012), pp. 5489–5503.

[26]
Luo, H., Xia, Y.D., Spiegel, S., Nourgaliev, R., Jiang, Z.G., A reconstructed discontinuous Galerkin method based on a Hierarchical WENO reconstruction for compressible flows on tetrahedral grids, J. Comput. Phys., 236(2013), pp. 477–492.

[27]
Cockburn, B., Gopalakrishnan, J., Lazarov, R., Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems, SIAM J. Numer. Anal., 47(2009), pp. 1319–1365.

[28]
Nguyen, N.C., Peraire, J., Cockburn, B., An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations, J. Comput. Phys., 228(2009), pp. 3232–3254.

[29]
Kroll, N., ADGIMA, A European project on the development of adaptive higher-order variational methods for aerospace applications, AIAA-2009-176.

[31]
Leicht, T., Hartmann, R., Error estimation and anisotropic mesh refinement for 3D laminar aerodynamic flow simulations, J. Comput. Phys., 229(2010), pp. 7344–7360.

[32]
Cheng, J., Yang, X.Q., Liu, T.G., Luo, H., A direct discontinuous Galerkin method for the compressible Navier-Stokes equations on arbitrary grids, AIAA-2016-1344.

[33]
Karypis, G., Kumar, V., Metis-unstructured graph partitioning and sparse matrix ordering system, version 2.0, 1995.

[34]
Yang, X.Q., Cheng, J., Wang, C.J., Luo, H., Si, J.T., A fast, implicit discontinuous Galerkin method based on analytical Jacobians for the compressible Navier-Stokes equations, AIAA-2016-1326.

[35]
Castonguay, P., High-order energy stable flux reconstruction schemes for fluid flow simulations on unstructured grids, Ph.D. thesis, Stanford University, 2012.

[36]
Liu, H.L., Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations, Math. Comp., 84(2015), pp. 2263–2295.

[37]
Cao, W.-X., Liu, H.L., Zhang, Z.-M., Superconvergence of the direct discontinuous Galerkin method for convection-diffusion equations, Numer. Methods Partial Differential Eq., doi:10.1002/num.22087, 2016.