title: ÐÐ¿Ð¾ÑÑÐµÑÐ¸Ð¾ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸ Ð¿ÑÐ¸Ð±Ð»Ð¸Ð¶ÐµÐ½Ð½ÑÑ ÑÐµÑÐµÐ½Ð¸Ð¹, Ð¿Ð¾Ð»ÑÑÐ°ÐµÐ¼ÑÑ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¼ÐµÑÐ¾Ð´Ð° ÑÐ¸ÐºÑÐ¸Ð²Ð½ÑÑ Ð¾Ð±Ð»Ð°ÑÑÐµÐ¹
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 posterori analysis of accuracy of solutions obtained by fictitious domain method
Creators: name: ÐÐ¾Ð·Ð»Ð¾Ð², ÐÐ¾ÑÐ¸Ñ
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Ð¾Ð½ÐµÑÐ½ÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð² Ð¼ÐµÑÐ¾Ð´
Ð¼ÐµÑÐ¾Ð´ ÑÐ¸ÐºÑÐ¸Ð²Ð½ÑÑ Ð¾Ð±Ð»Ð°ÑÑÐµÐ¹
Ð°Ð¿Ð¾ÑÑÐµÑÐ¸Ð¾ÑÐ½ÑÐµ Ð¾ÑÐµÐ½ÐºÐ¸ Ð¾ÑÐ¸Ð±Ð¾Ðº
fictitious domain method
a posteriori error estimates

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description: This paper is concerned with the a posteriori error analysis of the finite element solution of the homogenous Dirichlet boundary problem for an elliptic operator obtained by a fictitious domain method. We present a novel and fully computable a posteriori estimate for this numerical approach. The effectiveness of the derived error bound is demonstrated through a series of numerical experiments and case studies. The following tasks were completed as part of this research project: 1. Determining an accurate and computable a posteriori error bound for finite element solutions obtained with fictitious domain method. 2. Developing a reliable post-processing procedure of the numerical flux. The post-proccesed flux is essential for calculating the proposed error bound type. 3. Assessing the efficiency of proposed estimation technique. Overall, this work provides new means to conduct robust and efficient error analysis of finite element solutions for elliptic problems with complex or irregular geometry.