TY - JOUR T1 - A Split Least-Squares Characteristic Procedure for Convection-Dominated Parabolic Integro-Differential Equations AU - Guo , Hui AU - Fu , Hongfei JO - Communications in Mathematical Research VL - 1 SP - 1 EP - 14 PY - 2021 DA - 2021/05 SN - 31 DO - http://doi.org/10.13447/j.1674-5647.2015.01.01 UR - https://global-sci.org/intro/article_detail/cmr/18942.html KW - split least-square, characteristic, convection-dominated, convergence analysis. AB -
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.