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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 1D transport equation
P. A. Bakhvalov, M. D. Surnachev
Abstract:
We consider linear schemes with several degrees of freedom for the 1D 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 $q\geqslant p$ (for the discontinuous Galerkin method $p = k+1$ and $q = 2k+1$ where $k$ is the order of polynomials). We prove that this estimate holds if and only if there exists 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 $O(h^p)$. This fact leads to an algorithm establishing the optimal values $p$ and $q$ for a given scheme.
Keywords:
consistency and accuracy, superconvergence.
Citation:
P. A. Bakhvalov, M. D. Surnachev, “Linear schemes with several degrees of freedom for the 1D transport equation”, Keldysh Institute preprints, 2019, 073, 40 pp.
Linking options:
https://www.mathnet.ru/eng/ipmp2711 https://www.mathnet.ru/eng/ipmp/y2019/p73
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Abstract page: | 105 | Full-text PDF : | 21 | References: | 11 |
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