Approximation of parabolic PDEs on spheres using spherical basis functions
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Publication:1774027
DOI10.1007/s10444-003-3960-9zbMath1065.35024OpenAlexW2169211733MaRDI QIDQ1774027
Publication date: 29 April 2005
Published in: Advances in Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10444-003-3960-9
Heat equation (35K05) Theoretical approximation in context of PDEs (35A35) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22)
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Cites Work
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- Finite elements on the sphere
- Stability results for scattered-data interpolation on Euclidean spheres
- A standard test set for numerical approximations to the shallow water equations in spherical geometry
- Distributing many points on a sphere
- Error bounds for solving pseudodifferential equations on spheres by collocation with zonal kernels
- \(L_{p}\)-error estimates for radial basis function interpolation on the sphere
- Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
- Positive definite functions on spheres
- Strictly Positive Definite Functions on Spheres
- Error estimates for scattered data interpolation on spheres
- Norm estimates of interpolation matrices and their inverses associated with strictly positive definite functions
- Equidistribution on the Sphere
- Scattered Data Interpolation on Spheres: Error Estimates and Locally Supported Basis Functions
- From finite differences to finite elements. A short history of numerical analysis of partial differential equations