CONSTRUCTION OF BASIS FUNCTIONS FOR FINITE ELEMENT METHODS

Authors

Doniyorov N. N. Asia International University, 74, Gijduvon str., Bukhara 200114, Uzbekistan

Keywords:

Basis functions, ordinary differential equation, boundary value problem, finite element, optimal interpolation formula, error functional, Hilbert space.

Abstract

In this work, we study the problem of constructing basis functions for finite element methods. In this case, we use the coefficients of the algebraic-trigonometric optimal interpolation formula constructed using the Sobolev method in the Hilbert space of differentiable functions. In addition, we will prove the theorem expressing the main property of these local basis functions.

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References

Doniyorov N. N. Algebro-trigonometric optimal interpolation formula in a Hilbert space. Problems of computational and applied mathematics, no. 3/1 (50), 2023. Pp. 5-19.

Hayotov A. R., Doniyorov N. N. Modern problems of applied mathematics and information technology, Bukhara, 2024. AIP Conference Proceedings. -pp. 06051-1–06051-11. https://doi.org/10.1063/5.0199916

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Published

2026-04-21

How to Cite

Doniyorov N. N. (2026). CONSTRUCTION OF BASIS FUNCTIONS FOR FINITE ELEMENT METHODS. International Multidisciplinary Journal for Research & Development, 13(4), 1073–1075. Retrieved from https://ijmrd.in/index.php/imjrd/article/view/5762