A Split Least-Squares Characteristic Procedure for Convection-Dominated Parabolic Integro-Differential Equations
Year: 2015
Author: Hui Guo, Hongfei Fu
Communications in Mathematical Research , Vol. 31 (2015), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2015.01.01
Communications in Mathematical Research , Vol. 31 (2015), Iss. 1 : pp. 1–14
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: split least-square characteristic convection-dominated convergence analysis.