Convergence Rate of the Spectral Difference Method on Regular Triangular Meshes

We consider the spectral difference method based on the \(p\) th order Raviart–Thomas space ( \(p=1,2,3\) ) on regular triangular meshes for the scalar transport equation. The solution converges with the order \(p\) if the transport velocity is parallel to a family of mesh edges and with the order \(p+1\) otherwise. We prove this fact for \(p=1\) and show it for \(p=1,2,3\) in numerical experiments.