A Provably Stable Discontinuous Galerkin Spectral Element Approximation for Moving Hexahedral Meshes

A Polynomial Spectral Calculus for Analysis of DG Spectral Element Methods

“…We use the calculus now to show that it is stable if the coefficient matrices à are constant. If, in addition, characteristic boundary conditions are used at physical boundaries, the approximation is optimally stable in the sense that the global energy discretely matches (21).…”

“…To match the PDE energy bound, ( 21), the fully upwind flux must be used at the physical boundaries. With exterior values g set along incoming characteristics [21] and when σ = 1,…”