A Split Least-Squares Characteristic Procedure for Convection-Dominated Parabolic Integro-Differential Equations (Communications in Mathematical Research, 2021)
In this paper, we combine a split least-squares procedure with the methodof characteristics to treat convection-dominated parabolic integro-differential equations. By selecting the least-squares functional properly, the procedure can be splitinto two independent sub-procedures, one of which is for the primitive unknown andthe 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 estimatefor $σ$. Numerical results are presented to substantiate the validity of the theoreticalresults.