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.