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.

翻译：这项工作的目的是详细描述Spectral Dreaction Raviart-Thomas(SDRT)配方对二维和三维抗拉产品元素和简单度的二维和三维抗拉产品元素的开发情况。通过这一过程,作者根据通量的线性性和网状一致性的假设,确定了SDR方法与Flus-Rebuilt(FR)方法之间的等值。这种连接使得FR方案能够为两种和三维简单度的简单度建立新的组合,并恢复了众所周知的FR-SD方法,并带有抗拉产品元素。此外,对上述两种方案的数字消散和分解方法以及交替性G-DR(FR-DG)方法的分解和分解方法的分解方法进行了透彻分析。SDRT展示了SDR-DF的分解和分散性差。最后,研究的结论是,SDRT的分解和Slive-T的分母体-Slix-Slievral-ral-ral-rual-ral-ral-reval-reval-reval-ral-ral-ration-revlation-Lislation-Lisal-Lislal-Lisal-I-Lisal-Lisal-Supal-I 和后演算为SU-I-I-I-I-I-I-I-Slation-T-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-I-