Semi-Lagrangian difference approximations for distinct transfer operators

Тип публикации: доклад, тезисы доклада, статья из сборника материалов конференций

Конференция: 10th 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 approximations 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.

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Издание

Журнал: AIP Conference Proceedings

Выпуск журнала: 2025

Номера страниц: 020004

Издатель: American Institute of Physics Inc.

Авторы

  • Shaydurov V. (Tianjin University of Finance and Economics)
  • Efremov A. (Institute of Computational Modeling,SB RAS)
  • Gileva L. (Institute of Computational Modeling,SB RAS)

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