Convergence and Stability of Explicit/Implicit Schemes for Parabolic Equations with Discontinuous Coefficients
Year: 2004
Author: Shaohong Zhu, Guangwei Yuan, Weiwei Sun
International Journal of Numerical Analysis and Modeling, Vol. 1 (2004), Iss. 2 : pp. 131–146
Abstract
In this paper an explicit/implicit schemes for parabolic equations with discontinuous coefficients is analyzed. We show that the error of the solution in $L^∞$ norm and the error of the discrete flux in $L^2$ norm are in order $O(\tau + h^2)$ and $O(\tau + h^{\frac{3}{2}})$, respectively and the scheme is stable under some weaker conditions, while the difference scheme has the truncation error $O(1)$ at the neighboring points of the discontinuity of the coefficient. Numerical experiments, which are given for both linear and nonlinear problems, show that our theoretical estimates are optimal in some sense. The comparison with some classical scheme is presented.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2004-IJNAM-970
International Journal of Numerical Analysis and Modeling, Vol. 1 (2004), Iss. 2 : pp. 131–146
Published online: 2004-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Domain decomposition parabolic equations discontinuous coefficient parallel difference schemes convergence.