An Adaptive Wavelet Collocation Method for Solution of the Convection-Dominated Problem on a Sphere

In this paper, we present a numerical simulation of a convection-dominated problem using adaptive wavelet collocation method. This is based on second-generation spherical wavelets on a recursively refined spherical geodesic grid. The power lies in the fact that they only require small number of coefficients to represent this problem more accurately, which allows compression and efficient computation. In contrast with other approximate schemes, this approach reduced the number of collocation points used by factors of many orders of magnitude when compared to uniform grids of equivalent resolution. Numerical results demonstrate the efficiency of our approach.