Interpolation of the Function of Two Variables with Large Gradients in the Boundary Layers
The problem of interpolation for the function of two variables with large gradients in the boundary layers is investigated. It is suggested that the function can be represented as a sum of a regular component with bounded derivatives up to some order and of two boundary layer components. The boundar...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2015-06-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | https://kpfu.ru/portal/docs/F1578677601/157_2_phys_mat_5.pdf |
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| _version_ | 1846093246719066112 |
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| author | A.I. Zadorin |
| author_facet | A.I. Zadorin |
| author_sort | A.I. Zadorin |
| collection | DOAJ |
| description | The problem of interpolation for the function of two variables with large gradients in the boundary layers is investigated. It is suggested that the function can be represented as a sum of a regular component with bounded derivatives up to some order and of two boundary layer components. The boundary layer components are known, but their coefficients are uncertain. Such representation is typical for the solution of a singular perturbed elliptic problem. A two-dimensional interpolation formula, which is exact on the boundary layer components, is deduced. The formula has the arbitrary number of nodes in each direction. The accuracy estimate, which is uniform in gradients of the interpolated function in the boundary layers, is proved. The results of numerical experiments are provided. |
| format | Article |
| id | doaj-art-a9bacfa541ab46bdbdc841a7b076e28b |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2015-06-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-a9bacfa541ab46bdbdc841a7b076e28b2025-01-02T18:14:49ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982015-06-0115725567Interpolation of the Function of Two Variables with Large Gradients in the Boundary LayersA.I. Zadorin0Sobolev Institute of Mathematics, Omsk Branch, Omsk, 644099 RussiaThe problem of interpolation for the function of two variables with large gradients in the boundary layers is investigated. It is suggested that the function can be represented as a sum of a regular component with bounded derivatives up to some order and of two boundary layer components. The boundary layer components are known, but their coefficients are uncertain. Such representation is typical for the solution of a singular perturbed elliptic problem. A two-dimensional interpolation formula, which is exact on the boundary layer components, is deduced. The formula has the arbitrary number of nodes in each direction. The accuracy estimate, which is uniform in gradients of the interpolated function in the boundary layers, is proved. The results of numerical experiments are provided.https://kpfu.ru/portal/docs/F1578677601/157_2_phys_mat_5.pdffunction of two variableslarge gradientsboundary layer componentnonpolynomial interpolationerror estimation |
| spellingShingle | A.I. Zadorin Interpolation of the Function of Two Variables with Large Gradients in the Boundary Layers Учёные записки Казанского университета: Серия Физико-математические науки function of two variables large gradients boundary layer component nonpolynomial interpolation error estimation |
| title | Interpolation of the Function of Two Variables with Large Gradients in the Boundary Layers |
| title_full | Interpolation of the Function of Two Variables with Large Gradients in the Boundary Layers |
| title_fullStr | Interpolation of the Function of Two Variables with Large Gradients in the Boundary Layers |
| title_full_unstemmed | Interpolation of the Function of Two Variables with Large Gradients in the Boundary Layers |
| title_short | Interpolation of the Function of Two Variables with Large Gradients in the Boundary Layers |
| title_sort | interpolation of the function of two variables with large gradients in the boundary layers |
| topic | function of two variables large gradients boundary layer component nonpolynomial interpolation error estimation |
| url | https://kpfu.ru/portal/docs/F1578677601/157_2_phys_mat_5.pdf |
| work_keys_str_mv | AT aizadorin interpolationofthefunctionoftwovariableswithlargegradientsintheboundarylayers |