(untitled) (Communications in Mathematical Research, 2021)
In this paper, we combine a split least-squares procedure with the method of characteristics to treat convection-dominated parabolic integro-differential equations. By selecting the least-squares functional properly, the procedure can be split into two independent sub-procedures, one of which is for the primitive unknown and the other is for the flux. Choosing projections carefully, we get optimal order H^1 (Ω) and L^2 (Ω) norm error estimates for u and sub-optimal (L^2 (Ω))^d norm error estimate for σ. Numerical results are presented to substantiate the validity of the theoretical results.