Adaptive Refinement of the Variational Grid Method

Autor:	Yu. K. Dem'yanovich, N. A. Lebedinskaya, A. N. Terekhov
Rok vydání:	2022
Předmět:	Artificial Intelligence Control and Systems Engineering General Mathematics
Zdroj:	WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL. 17:527-534
ISSN:	2224-2856 1991-8763
DOI:	10.37394/23203.2022.17.58
Popis:	In this paper, we have developed a new approach to the local improvement of an approximate solution which has been obtained with the finite element method. The proposed improvement is adaptive, and it minimizes the energy functional. The discussed algorithm can be implemented analytically as well as numerically. The proposed approach can be applied to the adaptive refinement of the previously calculated variational grid approximation. The proposed method allows you to expand the approximate space by adding new coordinate functions. The implementation of a local approximation requires a small amount of arithmetic operations. The number of arithmetic operations does not depend on the number of nodes of the previously calculated approximation. Examples of the implementation of the method are considered for a problem with strong degeneracy and for a problem without degeneracy.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::ff20746a0199149c895cb1aecfb9a40c https://doi.org/10.37394/23203.2022.17.58 Zobrazit plný text záznamu