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