Numerical comparison of least square-based finite-difference (LSFD) and radial basis function-based finite-difference (RBFFD) methods

In this paper, two mesh-free methods, i.e., least square-based finite difference (LSFD) and radial basis function-based finite difference (RBFFD), are compared numerically in terms of their accuracy and efficiency. These two mesh-free methods are based on different approximation schemes, that is, the least square approximation and radial basis function (RBF) approximation. The two mesh-free methods exhibit very different behaviors in many ways. In this study, we examine the performance of the two methods by applying them to two example problems: Poisson equation and two-dimensional incompressible viscous lid-driven cavity flow, and some interesting findings are observed.