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 - <p style="text-align: justify;">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.</p>