This study addresses linear dispersion–diffusion analysis for the spectral/hp continuous
Galerkin (CG) formulation in one dimension. First, numerical dispersion and diffusion
curves are obtained for the advection–diffusion problem and the role of multiple
eigencurves peculiar to spectral/hp methods is discussed. From the eigencurves’ behaviour,
we observe that CG might feature potentially undesirable non-smooth dispersion/diffusion
characteristics for under-resolved simulations of problems strongly dominated by either
convection or diffusion. Subsequently, the linear advection equation augmented with
spectral vanishing viscosity (SVV) is analysed. Dispersion and diffusion characteristics of
CG with SVV-based stabilization are verified to display similar non-smooth features in
flow regions where convection is much stronger than dissipation or vice-versa, owing to
a dependency of the standard SVV operator on a local Péclet number. First a modification
is proposed to the traditional SVV scaling that enforces a globally constant Péclet number
so as to avoid the previous issues. In addition, a new SVV kernel function is suggested
and shown to provide a more regular behaviour for the eigencurves along with a
consistent increase in resolution power for higher-order discretizations, as measured by
the extent of the wavenumber range where numerical errors are negligible. The dissipation
characteristics of CG with the SVV modifications suggested are then verified to be broadly
equivalent to those obtained through upwinding in the discontinuous Galerkin (DG)
scheme. Nevertheless, for the kernel function proposed, the full upwind DG scheme is
found to have a slightly higher resolution power for the same dissipation levels. These
results show that improved CG-SVV characteristics can be pursued via different kernel
functions with the aid of optimization algorithms.