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- Title
Linear schemes with several degrees of freedom for the transport equation and the long-time simulation accuracy.
- Authors
Bakhvalov, Pavel; Surnachev, Mikhail
- Abstract
We consider linear schemes with several degrees of freedom for the transport equation on uniform meshes. For these schemes, the solution error is |$O(h^p + th^q)$| , where |$p$| is equal to or greater by one than the order of the truncation error 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 |$O(h^p)$|. In a one-dimensional case, this mapping can be found in the class of local mappings. In more dimensions, the existence of a local mapping with such properties is guaranteed only under additional assumptions.
- Publication
IMA Journal of Numerical Analysis, 2024, Vol 44, Issue 1, p297
- ISSN
0272-4979
- Publication type
Article
- DOI
10.1093/imanum/drad006