Abstract
In the paper, a new discrete analogue of an initial-boundary value problem is presented for the two-dimensional advection equation arising from a scalar time-dependent hyperbolic conservation law. At each time level, an approximate solution is found as a bilinear function on a uniform rectangular grid. For the presented scheme, a discrete analogue of the local integral balance equation is valid between two neighboring time levels. The numerical experiments are discussed for a solution with strong gradients.
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The work is supported by RFBR (Project 14-01-00296).
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Efremov, A., Karepova, E., Shaidurov, V. (2017). A Conservative Semi-Lagrangian Method for the Advection Problem. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2016. Lecture Notes in Computer Science(), vol 10187. Springer, Cham. https://doi.org/10.1007/978-3-319-57099-0_35
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DOI: https://doi.org/10.1007/978-3-319-57099-0_35
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