A Kernel-Based Least-Squares Collocation Method for Surface Diffusion

There are plenty of applications and analysis for time-independent elliptic partial differential equations in the literature hinting at benefits overtesting by using more collocation conditions than number basis functions. Overtesting not only reduces problem size, but is also known to be necessary stability convergence widely used unsymmetric Kansa-type strong-form methods. We consider kernel-based meshfree methods, which a method lines with spatially, solving parabolic on surfaces without parametrization. In this paper, we extend theories techniques smooth closed surfaces.