CONSTRUCTING NONLOCAL FUNDAMENTAL SPLINES
DOI:
https://doi.org/10.55640/Keywords:
Interpolation, optimal interpolation formula, error functional, Hilbert space, approximation, fundamental spline, finite elements, Sobolev method.Abstract
In this work, we study the problem of constructing nonlocal fundamental splines on rectangular finite elements. 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 nonlocal fundamental splines.
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References
1.Mitchell A. R., Wait R. The finite element method in partial differential equations (in Russian). Moscow, Mir, 1981.
2.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.
3.Zavyalov Yu. S., Kvasov B. I., Miroshnichenko V. L. Methods of spline functions (in Russian). Moscow, Nauka, 1980.
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