Commun. Math. Res., 31 (2015), pp. 1-14.
Published online: 2021-05
Cited by
- BibTex
- RIS
- TXT
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.
}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2015.01.01}, url = {http://global-sci.org/intro/article_detail/cmr/18942.html} }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.