title: ÐÐ¿Ð¾ÑÑÐµÑÐ¸Ð¾ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¿ÑÐ¸Ð±Ð»Ð¸Ð¶ÐµÐ½Ð½ÑÑ ÑÐµÑÐµÐ½Ð¸Ð¹ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÑ Ð·Ð°Ð´Ð°Ñ ÑÐµÐ¾ÑÐ¸Ð¸ Ð¶Ð¸Ð´ÐºÐ¾ÑÑÐ¸
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: A posteriori analysis of approximate solutions to nonlinear problems of fluid theory
Creators: name: Ð¨Ð°Ð¾ Ð¦Ð·ÑÑÐ¸
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2024
Subjects: ÐÐ¸Ð´ÐºÐ¾ÑÑÐ¸ Ð²ÑÐ·ÐºÐ¸Ðµ
Ð¶Ð¸Ð´ÐºÐ¾ÑÑÑ ÐÐ¸Ð½Ð³Ð°Ð¼Ð°
ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ
Ð°Ð´Ð°Ð¿ÑÐ¸Ð²Ð½ÑÐ¹ Ð¼ÐµÑÐ¾Ð´
Ð°Ð¿Ð¾ÑÑÐµÑÐ¸Ð¾ÑÐ½Ð°Ñ Ð¾ÑÐµÐ½ÐºÐ°
Bingham liquid
numerical methods
adaptive method
posteriori estimation

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description: The topic of the final qualifying work: A posteriori analysis of approximate solutions to nonlinear problems of fluid theory. This work is devoted to the analysis of a nonlinear boundary value problem in mathematical physics, the study of guaranteed and fully computable a posteriori estimates for a nonlinear viscous model associated with the antiplane flow of a non-Newtonian fluid (Bingham fluid) in a pipe. Tasks that were solved during the work: 1. Obtaining guaranteed and computable a posteriori estimates for minimizer approximations constructed using the Uzawa algorithm. 2. Checking the efficiency index of the received a posteriori assessment and error indication. 3. Implementation of the adaptive algorithm. The results of numerical experiments confirmed that this nonlinear Bingham fluid model has a free boundary, and showed that the efficiency index of the obtained majorant does not exceed 2 and the majorant gives a correct idea of the error distribution along the flows. Based on the indication, a complete adaptive algorithm is implemented, which consists of the following steps: 1. The initial grid â¦0 is set for k = 0. 2. Having solved the original problem, we get the vk solution. 3. Using the indicator, we mark the elements that require clarification. 4. Get a new grid â¦k+1 and go back to step 2.