Least-squares RBF-FD method for the incompressible Stokes equations with the singular source

In this article, we propose the least-squares RBF-FD method for the incompressible Stokes equations with the singular source along the interface. First, we apply Green's formula to derive interface conditions, then by employing the RBF-FD method to directly discretize the spatial operators, a least-squares system about the incompressible Stokes equations with interface conditions is constructed. The discrete least-squares system is derived by introducing the weight coefficient. We obtain the error bound of discrete least-squares system using the RBF interpolant theorem. Some numerical examples are provided to show the convergency and efficiency of the least-squares RBF-FD method for the incompressible Stokes equations with the singular source.