A fully discretised filtered polynomial approximation on spherical shells
This work provides a constructive numerical method for approximating functions on spherical shells, relevant for applications in geophysics or astrophysics, but the results are incremental and theoretical.
The paper develops a fully discretised filtered polynomial approximation on spherical shells, achieving algebraic decay of the approximation error in the supremum norm for functions with sufficient differentiability, as supported by numerical experiments.
A fully implementable filtered polynomial approximation on spherical shells is considered. The method proposed is a quadrature-based version of a filtered polynomial approximation. The radial direction and the angular direction of the shells are treated separately with constructive filtered polynomial approximation. The approximation error with respect to the supremum norm is shown to decay algebraically for functions in suitable differentiability classes. Numerical experiments support the results.