Matrix‐valued radial basis functions for the Lamé system
The problem of finding an approximate particular solution of an elliptic system of partial differential equations is considered. To construct the approximation, the differential operator is applied to a vector of radial basis functions. The resulting vectors are linearly combined to interpolate the...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2018-11, Vol.41 (16), p.6080-6107 |
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| container_title | Mathematical methods in the applied sciences |
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| creator | Grzhibovskis, R. Michel, C. Rjasanow, S. |
| description | The problem of finding an approximate particular solution of an elliptic system of partial differential equations is considered. To construct the approximation, the differential operator is applied to a vector of radial basis functions. The resulting vectors are linearly combined to interpolate the function on the right hand side. The solvability of the interpolation problem is established. Additionally, stability, and accuracy estimates for the method are given. These theoretical results are illustrated on several numerical examples related to the Lamé system. |
| doi_str_mv | 10.1002/mma.5121 |
| format | Article |
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To construct the approximation, the differential operator is applied to a vector of radial basis functions. The resulting vectors are linearly combined to interpolate the function on the right hand side. The solvability of the interpolation problem is established. Additionally, stability, and accuracy estimates for the method are given. 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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Basis functions Interpolation Lamé system Mathematical analysis matrix‐valued RBF Operators (mathematics) Partial differential equations particular solutions Radial basis function |
| title | Matrix‐valued radial basis functions for the Lamé system |
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