CONSTRUCTION OF BASIS FUNCTIONS FOR FINITE ELEMENT METHODS
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.
Keywords
Basis functions, ordinary differential equation, boundary value problem, finite element, optimal interpolation formula, error functional, Hilbert space.
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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