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This article is cited in 1 scientific paper (total in 1 paper)
Linear schemes with several degrees of freedom for the multidimensional transport equation
P. A. Bakhvalov, M. D. Surnachev
Abstract:
We consider linear schemes with several degrees of freedom for the transport equation. The solution error possesses the estimate $O(h^p + th^q)$ where $p$ is equal to or greater by one than the truncation error order and $q\geqslant p$. We prove the existence of a mapping of smooth functions on the mesh space providing the $q$-th order of the truncation error and deviating from the standard mapping ($L_2$-projection for example) by the order $h^p$. In contrast with 1D case local mapping with such properties generally does not exist. We prove sufficient existence conditions.
Keywords:
consistency and accuracy, superconvergence.
Citation:
P. A. Bakhvalov, M. D. Surnachev, “Linear schemes with several degrees of freedom for the multidimensional transport equation”, Keldysh Institute preprints, 2019, 074, 44 pp.
Linking options:
https://www.mathnet.ru/eng/ipmp2712 https://www.mathnet.ru/eng/ipmp/y2019/p74
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Abstract page: | 132 | Full-text PDF : | 30 | References: | 13 |
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