  The purpose of this work is to describe in detail the development of the
Spectral Difference Raviart-Thomas (SDRT) formulation for two and
three-dimensional tensor-product elements and simplexes. Through the process,
the authors establish the equivalence between the SDRT method and the
Flux-Reconstruction (FR) approach under the assumption of the linearity of the
flux and the mesh uniformity. Such a connection allows to build a new family of
FR schemes for two and three-dimensional simplexes and also to recover the
well-known FR-SD method with tensor-product elements. In addition, a thorough
analysis of the numerical dissipation and dispersion of both aforementioned
schemes and the nodal Discontinuous Galerkin FR (FR-DG) method with two and
three-dimensional elements is proposed through the use of the combined-mode
Fourier approach. SDRT is shown to possess an enhanced temporal linear
stability regarding the FR-DG. On the contrary, SDRT displays larger
dissipation and dispersion errors with respect to FR-DG. Finally, the study is
concluded with a set of numerical experiments, the linear advection-diffusion
problem, the Isentropic Euler Vortex and the Taylor-Green Vortex (TGV). The
latter test case shows that SDRT schemes present a non-linear unstable behavior
with simplex elements and certain polynomial degrees. For the sake of
completeness, the matrix form of the SDRT method is developed and the
computational performance of SDRT with respect to FR schemes is evaluated using
GPU architectures.
