Тип публикации: доклад, тезисы доклада, статья из сборника материалов конференций
Конференция: International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2018; Albena; Albena
Год издания: 2018
Идентификатор DOI: 10.1063/1.5064877
Ключевые слова: conservation laws, continuity equation, parabolic differential equation, semi-Lagrangian approximation, Stability and convergence, transfer operator
Аннотация: The paper gives a review of using the semi-Lagrangian approximation depending on the fulfillment of conservation laws for the transfer operator. We begin with approximations of the one-dimensional transfer equation and a parabolic one as simple methodological examples. For two-dimensional problems, first we apply one-dimensional apПоказать полностьюproximations in two directions separately. Then we present another combined approximation along trajectories of the transfer operator. For parabolic and transfer equations, the principles of constructing discrete analogues are demonstrated for three different conservation laws of transfer operator (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 distinct difference problems as well as distinct ways to justify their stability.
Журнал: AIP Conference Proceedings
Выпуск журнала: 2025
Номера страниц: 020004
Издатель: American Institute of Physics Inc.