  Motivated by classical vortex blob methods for the Euler equations, we
develop a numerical blob method for the aggregation equation. This provides a
counterpoint to existing literature on particle methods. By regularizing the
velocity field with a mollifier or "blob function", the blob method has a
faster rate of convergence and allows a wider range of admissible kernels. In
fact, we prove arbitrarily high polynomial rates of convergence to classical
solutions, depending on the choice of mollifier. The blob method conserves mass
and the corresponding particle system is both energy decreasing for a
regularized free energy functional and preserves the Wasserstein gradient flow
structure. We consider numerical examples that validate our predicted rate of
convergence and illustrate qualitative properties of the method.
