A Split Least-Squares Characteristic Procedure for Convection-Dominated Parabolic Integro-Differential Equations

Abstract

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.