Adaptive wavelet-based methods for solution of PDEs

A dynamic adaptive numerical method for solving partial differential equations (PDEs) on the sphere is necessary to solve problems with localized structures or sharp transitions. The numerical solution of such problems on uniform grids is impractical, since high-resolution computations are required only in regions where sharp transitions occur. An adaptive wavelet collocation method provides a robust method for controlling spatial grid adaptation -- fine grid spacing in regions where a solution varies greatly (i.e., near steep gradients, or near-singularities) and a much coarser grid where the solution varies slowly, which I will discuss in this talk.