Abstract
The paper demonstrates different ways of using the semi-Lagrangian approximation depending on the fulfillment of conservation laws. A one-dimensional continuity equation and a parabolic one are taken as simple methodological examples. For these equations, the principles of constructing discrete analogues are demonstrated for three different conservation laws (or the requirements of stability in the related discrete norms similar to the L1, L2, L∞-norms). It is significant that different conservation laws yield difference problems of different types as well as different ways to justify their stability.
Funding: The different parts of this work were funded by Russian Foundation for Basic Research to projects No. 17-01-000270 and No. 16-41-243029 which was supported also by Government of Krasnoyarsk Territory, Krasnoyarsk Region Science and Technology Support Fund.
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