A Comparison of Radial Basis Function Finite Difference Methods for Approximating the Laplace-Beltrami Operator

There are many applications in science and engineering that involve partial differential equations (PDEs) on surfaces: chemical diffusion through cell membranes, chemical diffusion through the atmosphere etc. Often Solutions to PDEs cannot be represented analytically, and must be approximated using numerical techniques. This poser compares three Radial Basis Function Finite Difference (RBF-FD) methods that use scattered data to obtain high-order-accurate approximations of the Laplace-Beltrami operator (surface diffusion) - a common component of PDEs on surfaces.