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Pseudodifferential equations on the sphere with spherical splines. (English) Zbl 1298.65177

The authors solve strongly elliptic pseudodifferential equations on the sphere by the Galerkin method using spherical splines. The class of equations includes for instance the Laplace-Beltrami equation, the Stokes equation and weakly singular integral equations. They derive the optimal convergence rate of the approximation. Some numerical results are presented.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35S15 Boundary value problems for PDEs with pseudodifferential operators
41A15 Spline approximation
65D07 Numerical computation using splines
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