  This note proposes embedding a time dependent PDE into a convection-diffusion
type PDE (in one space dimension higher) with singularity, for which two
discretization schemes, the classical streamline-diffusion and the EAFE (edge
average finite element) one, are investigated in terms of stability and error
analysis. The EAFE scheme, in particular, is extended to be arbitrary order
which is of interest on its own. Numerical results, in combined space-time
domain demonstrate the feasibility of the proposed approach.
