A Skew-Symmetric Discontinuous Galerkin Spectral Element Discretization and Its Relation to SBP-SAT Finite Difference Methods

By Gregor J. Gassner. SIAM Journal on Scientific Computing, 2013

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Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces (2014, background): “Spectral collocation operators are readily expressed in SBP-SAT form [5, 22, 9, 17], although not all may be expressed as diagonal norm SBP operators; e.”
High‐order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations (2014, background): “In [35] and [36], skew symmetric formulations for nodal DG spectral element approximations are introduced as well.”
Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations (2016, methodology): “1 and is in accordance to similar observations [13, 14, 16].”
Review of summation-by-parts schemes for initial-boundary-value problems (2013, background): “For more details on relations to dG schemes, see [75].”
Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (2014, background): “There are many discrete operators that possess the SBP property; for example, Carpenter and Gottlieb [74] and Gassner [75] investigated the SBP property of pseudo-spectral collocated methods.”