Volume 31, Issue 1
A Split Least-Squares Characteristic Procedure for Convection-Dominated Parabolic Integro-Differential Equations

Commun. Math. Res., 31 (2015), pp. 1-14.

Published online: 2021-05

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• 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.

• Keywords

split least-square, characteristic, convection-dominated, convergence analysis.

35L15, 65M15, 65M60

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@Article{CMR-31-1, author = {Hui and Guo and and 18589 and and Hui Guo and Hongfei and Fu and and 18590 and and Hongfei Fu}, title = {A Split Least-Squares Characteristic Procedure for Convection-Dominated Parabolic Integro-Differential Equations}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {31}, number = {1}, pages = {1--14}, 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.

}, 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} }
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.

Hui Guo & Hongfei Fu. (2021). A Split Least-Squares Characteristic Procedure for Convection-Dominated Parabolic Integro-Differential Equations. Communications in Mathematical Research . 31 (1). 1-14. doi:10.13447/j.1674-5647.2015.01.01
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