Recovering Grid-Point Values Without Gibbs Oscillations In Two Dimensional Domains On The Sphere

Spectral methods using spherical harmonic basis functions have proven to be very effective in geophysical and astrophysical simulations. It is an unfortunate fact, however, that spurious oscillations, known as the Gibbs phenomenon, contaminate these spectral solutions, particularly in regions where discontinuities or steep gradients occur. They are also apparent in the polar regions even when considering analytical periodic functions. These undesirable artificial oscillations have been the topic of several recent articles [8],[17],[19]. Navarra et.al. [19] alleviates the problem by employing various filters in one and two dimensions. Lindberg and Broccoli [17] implement a nonuniform spherical smoothing spline and zonal filtering, while Gelb [8] applies the Gegenbauer method [13] in the latitudinal direction for fixed longitudinal coordinates. Since the physical problems solved on spheres often involve discontinuities or steep gradients in the longitudinal direction, and since spherical..