Approaches to constructing two-dimensional interpolation formulas in the presence of boundary layers

Approaches to constructing two-dimensional interpolation formulas in the presence of boundary layers Full article

Conference

15th International Scientific and Technical Conference: Applied Mechanics and Systems Dynamics
09-11 Nov 2021 , Омск

Journal

Journal of Physics: Conference Series
ISSN: 1742-6588 , E-ISSN: 1742-6596

Output data

Year: 2022, Volume: 2182, Number: 1, Article number : 012036, Pages count : DOI: 10.1088/1742-6596/2182/1/012036

Authors

Zadorin A.I. ¹

Affiliations

1	Sobolev Institute of Mathematics, pr. Koptyuga, 4, Novosibirsk, 630090, Russian Federation

Funding (2)

1	Омский филиал ФГБУН «Институт математики им. С.Л. Соболева СО РАН».	FWNF-2022-0016
2	Russian Foundation for Basic Research	20-01-00650

An overview of approaches to the construction of two-dimensional interpolation formulas for a function of two variables with large gradients in the boundary layer regions is given. The problem is that the use of polynomial interpolation formulas on a uniform grid can lead to errors of the order of O(1). It is shown that the use of polynomial interpolation formulas on the Shishkin and Bakhvalov grids leads to the fact that the error becomes uniform in a small parameter. More accurate results are obtained by using the Bakhvalov grid. It is shown that on a uniform grid it is possible to successfully apply interpolation formulas that are exact on the singular components responsible for large function gradients in boundary layers. Numerical results are given. © Published under licence by IOP Publishing Ltd.

Zadorin A.I.
Approaches to constructing two-dimensional interpolation formulas in the presence of boundary layers
Journal of Physics: Conference Series. 2022. V.2182. N1. 012036 . DOI: 10.1088/1742-6596/2182/1/012036 Scopus РИНЦ OpenAlex

Scopus:	2-s2.0-85127650442
Elibrary:	48425922
OpenAlex:	W4220704868

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Scopus	4
OpenAlex	3
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